id
stringlengths 35
35
| setting_key
stringclasses 1
value | setting_name
stringclasses 0
values | messages
listlengths 1
1
| ground_truth
stringclasses 39
values | dataset
stringclasses 1
value |
|---|---|---|---|---|---|
algebra_polynomial_roots_train_0900
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let h(q) be the second derivative of -3773*q**6/3 + 6419*q**5/4 + 595*q**4/4 - 1965*q**3/2 + 945*q**2/2 - 43*q + 2. Let h(z) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_polynomial_roots_train_0901
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Express the second largest root of -12870*t**4 - 2899*t**2 + 21999*t**3 + 4104*t + 17296*t**2 + 4044*t**2 - 3744 - 14700*t = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
21
|
math
|
algebra_polynomial_roots_train_0902
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let k(q) be the second derivative of 440*q**6/3 - 6093*q**5/2 + 21393*q**4/2 - 10737*q**3 + 4617*q**2 - 1584*q. Suppose k(j) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14
|
math
|
algebra_polynomial_roots_train_0903
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let g(r) be the third derivative of 13*r**2 - 243/38*r**3 - 435/76*r**6 + 0 + 189/38*r**4 - 40/19*r**7 + 1737/380*r**5 + r. Express the second largest root of g(y) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
algebra_polynomial_roots_train_0904
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "If -15379*m**4 - 155168/9*m - 433147/9*m**3 - 137852/3*m**2 - 6656/3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_polynomial_roots_train_0905
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Express the second largest root of -3410*i**2 + 103 + 371 + 17640*i**4 + 246 + 30288*i**2 - 7578*i - 37352*i**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12
|
math
|
algebra_polynomial_roots_train_0906
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let h = -372639 - -1869189/5. Suppose 14436/5*j**3 - h*j + 243/2 + 5805/2*j**2 - 12474*j**4 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14
|
math
|
algebra_polynomial_roots_train_0907
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let v(f) = f**4 - f**3 - f**2 - f. Let b(d) = 12317*d**4 - 16953*d**3 + 8661*d**2 - 1941*d + 162. Let o = -90 + 88. Let u(m) = o*b(m) - 6*v(m). Let u(t) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_polynomial_roots_train_0908
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let w(h) be the first derivative of 0*h - 18 + 81/28*h**2 - 27/14*h**3 + 231/10*h**5 - 135/8*h**4. Suppose w(b) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_polynomial_roots_train_0909
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let -1836*y + 6912*y**4 - 65428*y**3 + 185214 - 24336*y**2 - 58942*y**4 + 185401 - 370345 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
algebra_polynomial_roots_train_0910
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let d(u) = 3*u**4 - u**3 - u**2 - 2*u + 1. Let m(s) be the first derivative of 11064*s**5/5 + 6797*s**4/2 - 5446*s**3/3 - 1153*s**2 + 694*s - 83. Let o(g) = -8*d(g) - m(g). Let o(v) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14
|
math
|
algebra_polynomial_roots_train_0911
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let y(q) = 113461 - 28048*q. Let c be y(4). Let 2214*i + 1512/5 - 4290*i**4 + 20127/5*i**2 - c*i**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
algebra_polynomial_roots_train_0912
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let k(z) = -9000*z**4 - 15125*z**3 - 2397*z**2 + 5463*z + 2037. Let g(t) = 99000*t**4 + 166375*t**3 + 26365*t**2 - 60090*t - 22405. Let h(i) = 6*g(i) + 65*k(i). Express the second largest root of h(l) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_polynomial_roots_train_0913
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Suppose -2130*v**2 + 11960/7*v - 25125/7*v**3 + 4800/7 + 17875/7*v**4 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
23
|
math
|
algebra_polynomial_roots_train_0914
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let z(r) be the second derivative of -23296*r**6/15 - 17832*r**5/5 - 2237*r**4 + 1103*r**3/3 + 780*r**2 + 9*r + 103. For the polynomial z(n), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9
|
math
|
algebra_polynomial_roots_train_0915
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let h(n) be the first derivative of -77*n**8/15 + 111*n**7/20 + 73*n**6/40 - 27*n**5/5 + 27*n**4/8 - 20*n**3/3 + 43. Let m(s) be the third derivative of h(s). Let m(d) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14
|
math
|
algebra_polynomial_roots_train_0916
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let h(r) be the second derivative of 209*r**7/14 + 7839*r**6/280 + 45*r**5/4 - 81*r**4/8 - 81*r**3/7 - 10*r**2 + 30*r. Let x(f) be the first derivative of h(f). For x(y) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
algebra_polynomial_roots_train_0917
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Find the value of n + m, where n/m is the second largest root of 6728*d**3 - 2349*d**2 + 381*d**2 + 540 + 29000*d**3 - 712*d - 47040*d**4 - 2564*d = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
17
|
math
|
algebra_polynomial_roots_train_0918
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let k(s) be the second derivative of -8192*s**7/875 + 2688*s**6/125 - 2592*s**5/125 + 54*s**4/5 - 81*s**3/25 - 60*s**2 - 40*s + 3. Let f(z) be the first derivative of k(z). Let f(i) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
19
|
math
|
algebra_polynomial_roots_train_0919
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Express the second largest root of -3085 + 16494*g - 101959*g**2 - 10465*g**4 + 20358*g - 6475*g**4 - 1091 + 92972*g**3 - 1117*g**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9
|
math
|
algebra_polynomial_roots_train_0920
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let x(f) be the first derivative of 114 - 363*f**5 + 621/16*f**2 - 81/2*f + 735/4*f**3 - 4587/32*f**4. If x(h) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14
|
math
|
algebra_polynomial_roots_train_0921
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let g(f) be the first derivative of 663*f**6/2 - 33133*f**5/35 + 88757*f**4/84 - 4148*f**3/7 + 1224*f**2/7 + 19*f - 60. Let d(x) be the first derivative of g(x). For the polynomial d(m), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
algebra_polynomial_roots_train_0922
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let v(y) be the first derivative of -858*y**5 - 1008*y**4 + 130*y**3/11 + 2808*y**2/11 + 864*y/11 - 916. Let v(x) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_polynomial_roots_train_0923
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let d(o) be the first derivative of -55*o**8/208 - 435*o**7/728 + 81*o**6/520 + 783*o**5/520 + 81*o**4/52 - 28*o**3/3 + 6. Let x(y) be the third derivative of d(y). For x(b) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
algebra_polynomial_roots_train_0924
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let w(y) be the third derivative of 0*y - 3077/16*y**4 - 76*y**2 + 69377/360*y**5 + 85*y**3 - 2431/21*y**7 + 0 + 1717/180*y**6. Express the second largest root of w(f) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
algebra_polynomial_roots_train_0925
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let v = -212 - -216. Let -8896*x**2 - 17754*x**4 - 13389*x**2 + 3894*x**v + 840*x - 34500*x**3 + 2205 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_polynomial_roots_train_0926
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let -7788*y - 72397*y**3 + 891 + 786*y + 4928*y**4 + 17823*y**2 + 55917*y**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
17
|
math
|
algebra_polynomial_roots_train_0927
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let t(s) be the first derivative of 2931/4*s**4 - 243/2*s**2 + 2714*s**3 - 4914*s**5 - 43 - 540*s. Suppose t(n) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
algebra_polynomial_roots_train_0928
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let f(d) = -7334*d**4 - 25313*d**3 - 29261*d**2 - 12736*d - 1612. Let c(l) = 4890*l**4 + 16875*l**3 + 19508*l**2 + 8491*l + 1075. Let n(h) = 8*c(h) + 5*f(h). Let n(k) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_polynomial_roots_train_0929
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let v(k) be the first derivative of -3762*k**5/5 + 4269*k**4/10 + 5081*k**3/10 - 747*k**2/10 - 108*k - 5010. If v(i) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
algebra_polynomial_roots_train_0930
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Suppose -33480/7 - 20520/7*u - 295275/7*u**3 + 83355/2*u**2 + 70125/14*u**4 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9
|
math
|
algebra_polynomial_roots_train_0931
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Suppose -6372/5*x**2 + 108 + 344*x**3 - 432/5*x + 2880*x**4 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
algebra_polynomial_roots_train_0932
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let l(y) be the first derivative of 30000*y**5/11 - 277875*y**4/22 + 6300*y**3/11 + 66015*y**2/11 + 14580*y/11 - 387. Find the value of n + m, where n/m is the second largest root of l(c) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
algebra_polynomial_roots_train_0933
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "For the polynomial 13392*s - 66836*s**4 - 4464/5 + 575484/5*s**3 - 323237/5*s**2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_polynomial_roots_train_0934
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "If 42442*t**3 + 83537*t**3 - 37235*t + 19328*t**4 - 806*t**4 - 9451*t + 35637*t**2 - 10440 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_polynomial_roots_train_0935
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Express the second largest root of -864/7 + 3904/7*c**3 + 72*c - 168960/7*c**4 + 27096/7*c**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
19
|
math
|
algebra_polynomial_roots_train_0936
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let l(d) be the third derivative of -819/220*d**5 + 315/44*d**4 + 0 + 189/22*d**3 + 30*d**2 + 2*d - 112/11*d**6 - 160/33*d**7. If l(w) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5
|
math
|
algebra_polynomial_roots_train_0937
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let o(v) be the third derivative of 11*v**8/14 + 8457*v**7/3640 + 297*v**6/104 + 999*v**5/520 + 81*v**4/104 - 32*v**3/3 - 26*v**2. Let y(a) be the first derivative of o(a). If y(z) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
algebra_polynomial_roots_train_0938
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let f be 171/(224523/(-1010)) - (186/13)/(-3). Express the second largest root of -4875*p**f - 10975/6*p**3 + 1365*p**2 + 90 + 1485/2*p = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_polynomial_roots_train_0939
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let j(l) be the first derivative of 121*l**8/12 + 2288*l**7/105 + 581*l**6/90 - 104*l**5/5 - 24*l**4 + 206*l**3/3 - 256. Let c(m) be the third derivative of j(m). Express the second largest root of c(w) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
algebra_polynomial_roots_train_0940
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let i(o) = -6*o**3 - 160*o**2 - 15*o - 1859. Let t be i(-27). Suppose 4576*r**t + 4300*r**3 - 540/11 - 2484/11*r + 7308/11*r**2 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
algebra_polynomial_roots_train_0941
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "For the polynomial 185289*w**3 + 78359*w**2 + 256813*w**2 + 179035*w**3 + 440331*w**4 + 11040 + 106376*w - 392283*w**4, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
math
|
algebra_polynomial_roots_train_0942
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Find the value of n + m, where n/m is the second largest root of 18858/5*l**2 - 3185*l**4 - 504*l - 945 + 1400*l**3 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
algebra_polynomial_roots_train_0943
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let b(q) = -q**4 - 2*q**3 - 3*q**2 + 1. Let t(p) = 11472*p**4 - 14776*p**3 + 4922*p**2 + 120*p - 141. Let d(r) = -3*b(r) + t(r). Suppose d(u) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
21
|
math
|
algebra_polynomial_roots_train_0944
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let p(h) be the first derivative of 21 + 891/10*h**2 + 1210*h**5 + 891/10*h - 1023/2*h**3 - 495*h**4. Let p(v) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
algebra_polynomial_roots_train_0945
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let b(k) be the second derivative of -675*k**6 - 11745*k**5/4 - 16245*k**4/4 - 749*k**3 + 2940*k**2 - 15*k - 4. If b(s) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_polynomial_roots_train_0946
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Express the second largest root of 1690 + 33600*v**4 - 2830*v + 1586 + 35440*v**3 + 1604*v**2 - 15460*v**2 - 8030*v = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
algebra_polynomial_roots_train_0947
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let 67093*g**3 - 14963*g**2 + 2078 - 4334*g**2 - 638 - 2027*g + 32955*g**4 - 3765*g**2 - 2869*g = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
16
|
math
|
algebra_polynomial_roots_train_0948
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let b(d) be the third derivative of 27*d**3 + 88/3*d**7 + 0*d - 92*d**2 + 0 - 307/20*d**6 + 99/8*d**4 - 639/20*d**5. For b(l) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_polynomial_roots_train_0949
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Suppose -45 = 2*k - 7*p, k + 66*p - 65*p - 9 = 0. If -6175*j**4 - 6705/8*j**k + 48565/8*j**3 - 2295/4*j + 135 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_polynomial_roots_train_0950
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let 93 - 83 + 2286*u - 1974*u**3 + 120 - 9000*u**4 + 140 - 4376*u**3 + 2490*u**2 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
17
|
math
|
algebra_polynomial_roots_train_0951
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let a be ((-2)/(-1) + 53)*1. Let k(c) = -330805*c**4 + 212680*c**3 + 136810*c**2 - 51840*c - 19385. Let o(f) = 12252*f**4 - 7877*f**3 - 5067*f**2 + 1920*f + 718. Let b(m) = a*o(m) + 2*k(m). If b(y) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_polynomial_roots_train_0952
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "If 1658*w**4 + 48872*w**2 + 45598*w**2 + 14352 + 4516*w**4 - 16252*w**2 - 60350*w - 38906*w**3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
22
|
math
|
algebra_polynomial_roots_train_0953
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Express the second largest root of 398110/9*x**2 + 13650*x**4 + 16650*x + 134770/3*x**3 + 2000 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_polynomial_roots_train_0954
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let 78806*b**4 + 54443*b**3 - 16920*b - 2880 + 31312*b**3 - 2382*b**2 - 7348*b**2 + 44044*b**4 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
math
|
algebra_polynomial_roots_train_0955
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let r(y) be the first derivative of 54*y + 11367/40*y**4 - 208*y**3 - 1611/20*y**2 + 12012/25*y**5 - 28. Suppose r(g) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14
|
math
|
algebra_polynomial_roots_train_0956
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let h(f) be the second derivative of 0 - 1089/5*f**5 - 11011/50*f**6 - 27/2*f**4 + 243/10*f**2 + 54*f**3 + 26*f. Find the value of n + m, where n/m is the second largest root of h(a) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_polynomial_roots_train_0957
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let d(i) be the third derivative of -16 + 117/8*i**3 - 1305/128*i**4 + 27/14*i**7 + 0*i - 3*i**2 + 2103/320*i**6 - 1729/320*i**5. Let d(c) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_polynomial_roots_train_0958
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let f = 38425 - 26310. For the polynomial 13913*q**3 - f*q**3 - 21276*q**2 - 34963*q**3 - 5808*q - 576 - 18150*q**4, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
math
|
algebra_polynomial_roots_train_0959
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let h(k) be the second derivative of 275*k**6/7 + 765*k**5/14 + 675*k**4/56 - 27*k**3/2 - 243*k**2/28 + k + 164. If h(z) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
math
|
algebra_polynomial_roots_train_0960
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Suppose 48 = 8*n + 16*n. Express the second largest root of 28662*q**4 + 810*q + 8827*q**4 + 324 - 309*q**4 - 6768*q**n - 9594*q**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
algebra_polynomial_roots_train_0961
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let t(a) = -84*a**2 + 933*a - 95. Let k be t(11). Express the second largest root of -252*b**3 - 6006*b**k + 324/7*b - 486/7 + 10368/7*b**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
16
|
math
|
algebra_polynomial_roots_train_0962
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let u(b) be the second derivative of -24*b**8/7 - 382*b**7/35 - 329*b**6/45 + 23*b**5/2 + 75*b**4/4 + 6*b**3 - 5*b. Let z(n) be the second derivative of u(n). Express the second largest root of z(o) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
math
|
algebra_polynomial_roots_train_0963
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let u(r) = -10643*r**4 + 25758*r**3 - 2491*r**2 - 5344*r + 1084. Let w(x) = 10641*x**4 - 25754*x**3 + 2490*x**2 + 5343*x - 1086. Let n(v) = 3*u(v) + 2*w(v). If n(b) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_polynomial_roots_train_0964
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let x(c) = -40247*c**4 - 49198*c**3 - 7695*c**2 + 7791*c + 2025. Let m(k) = -k**4 - 9*k**3 - 2*k. Let q(j) = 3*m(j) + x(j). Find the value of n + m, where n/m is the second largest root of q(p) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
math
|
algebra_polynomial_roots_train_0965
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let l(t) = t + 2. Let w be l(2). Suppose -196*i**w - 509*i**3 - 5804*i**4 + 3465*i**2 + 91 - 1141*i**3 + 351*i - 415 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
algebra_polynomial_roots_train_0966
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let s(v) = 422*v**5 - 13*v**4 - 477*v**3 + 324*v**2 - 79*v + 32. Let c(h) = -845*h**5 + 25*h**4 + 954*h**3 - 648*h**2 + 157*h - 65. Let w(u) = 2*c(u) + 5*s(u). Let r(p) be the first derivative of w(p). Find the value of n + m, where n/m is the second largest root of r(z) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
algebra_polynomial_roots_train_0967
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let r be 485 - (-4 - 2 - 2/(-1)). If -19250*s**4 + 7756*s**2 - 720 - 1200*s + 2853*s**3 + 5522*s**3 + r*s**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15
|
math
|
algebra_polynomial_roots_train_0968
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let l(h) be the second derivative of 440*h**7/21 - 395*h**6/12 - 139*h**5/10 + 237*h**4/4 - 45*h**3 - 4*h**2 - 68*h. Let m(s) be the first derivative of l(s). Suppose m(w) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
algebra_polynomial_roots_train_0969
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "If -2175 - 114102*m + 340011*m**2 + 15783 + 36720*m**4 - 313266*m**3 - 20196*m**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
algebra_polynomial_roots_train_0970
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let k(d) be the first derivative of 429*d**8/56 + 3491*d**7/280 - 301*d**6/30 - 1161*d**5/40 - 45*d**4/2 - 13*d**3/3 - 48. Let a(t) be the third derivative of k(t). If a(p) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
algebra_polynomial_roots_train_0971
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let n(c) be the second derivative of -7744*c**6/15 - 1056*c**5/5 + 5569*c**4/6 + 99*c**3 - 630*c**2 - 6674*c. Suppose n(m) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_polynomial_roots_train_0972
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let 83775/17*a**2 + 11076*a**3 + 15786/17*a + 1080/17 + 8619*a**4 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
algebra_polynomial_roots_train_0973
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let z(f) be the third derivative of 55*f**10/2646 - 265*f**9/5292 + 47*f**8/2352 + 53*f**7/980 - 3*f**6/35 + 7*f**5/30 + 33*f**2. Let a(y) be the third derivative of z(y). Let a(x) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15
|
math
|
algebra_polynomial_roots_train_0974
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let n(k) be the third derivative of 68*k**7/3 + 10343*k**6/120 - 689*k**5/5 + 129*k**4/8 + 63*k**3 + 177*k**2. Find the value of n + m, where n/m is the second largest root of n(v) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_polynomial_roots_train_0975
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let g(j) be the first derivative of -43 - 243/8*j + 945/8*j**3 + 567/16*j**2 - 3519/32*j**4 - 231*j**5. Find the value of n + m, where n/m is the second largest root of g(t) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14
|
math
|
algebra_polynomial_roots_train_0976
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let d(x) be the first derivative of 3344*x**5 - 22479*x**4/4 + 441*x**3 + 1080*x**2 - 324*x + 1380. For the polynomial d(h), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14
|
math
|
algebra_polynomial_roots_train_0977
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let t(n) be the second derivative of 160*n**6/3 - 226*n**5/3 + 15*n**4 + 114*n**3/5 - 72*n**2/5 - 4*n + 3. Express the second largest root of t(i) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_polynomial_roots_train_0978
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Express the second largest root of -217020/19*i**3 + 88296/19*i**2 + 15120/19 + 70200/19*i**4 + 98316/19*i = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12
|
math
|
algebra_polynomial_roots_train_0979
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let 1080 - 5163*g**2 + 8334*g**4 + 75171*g**3 + 5631*g**4 + 882*g - 2520*g**2 - 78195*g**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_polynomial_roots_train_0980
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let b(y) be the third derivative of 0 - 6*y**3 + 242/45*y**6 - 2*y**4 - 18*y**2 - 2662/135*y**7 + 0*y + 66/5*y**5. Suppose b(a) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14
|
math
|
algebra_polynomial_roots_train_0981
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let p(x) = -112311*x**4 + 101119*x**3 - 3321*x**2 - 14463*x + 2601. Let k(a) = 56156*a**4 - 50560*a**3 + 1660*a**2 + 7232*a - 1300. Let d(t) = -7*k(t) - 4*p(t). Let j(r) = -18717*r**4 + 16852*r**3 - 555*r**2 - 2409*r + 435. Let h(v) = 3*d(v) + 8*j(v). Suppose h(u) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
algebra_polynomial_roots_train_0982
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let i(r) = -43125*r**4 - 34211*r**3 - 859*r**2 + 4531*r + 869. Let x(q) = 2266*q + 434 - 6455*q**4 - 15107*q**4 - 11434*q**3 - 5672*q**3 - 430*q**2. Let g(d) = -2*i(d) + 5*x(d). Let g(z) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
math
|
algebra_polynomial_roots_train_0983
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Express the second largest root of 58707*g**2 - 266712*g**3 - 14288*g**4 + 15384*g - 7128 - 44617*g**4 + 15774*g = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
19
|
math
|
algebra_polynomial_roots_train_0984
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Express the second largest root of -2250*x**4 - 758 - 38*x**2 + 893 + 893*x**3 - 3018*x**3 + 657*x + 293*x**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
math
|
algebra_polynomial_roots_train_0985
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Suppose 1048959/23*q - 164160/23 - 24843/23*q**4 - 1359357/23*q**2 - 443079/23*q**3 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
16
|
math
|
algebra_polynomial_roots_train_0986
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let i(j) = 2 - 5*j. Let u be i(0). Find the value of n + m, where n/m is the second largest root of -28*p - 521*p - 108 + 3910*p**3 - 16*p**2 + 4400*p**4 + 163*p**u = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
math
|
algebra_polynomial_roots_train_0987
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let n(w) be the first derivative of 700*w**5 - 850*w**4 - 5500*w**3/3 + 3564*w**2 - 2016*w + 1599. Express the second largest root of n(c) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
algebra_polynomial_roots_train_0988
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let x(s) be the second derivative of 216*s**6/7 + 2277*s**5/10 + 247*s**4/4 - 3586*s**3/7 - 1035*s**2/2 + 179*s + 2. Let x(l) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5
|
math
|
algebra_polynomial_roots_train_0989
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let q be (138/(-18))/23*-12. Suppose 4050/13*v**2 + 1215/13 + 18000/13*v**3 - 20625/13*v**q - 6480/13*v = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14
|
math
|
algebra_polynomial_roots_train_0990
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Suppose -1642 + 1571*p**2 - 5112*p + 51822*p**3 + 202 + 4607*p**2 + 3750*p**2 + 43472*p**4 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
math
|
algebra_polynomial_roots_train_0991
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let n = 87743 + -87741. For the polynomial 375*f + 1041/11*f**n - 12558/11*f**3 - 11760/11*f**4 + 900/11, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
math
|
algebra_polynomial_roots_train_0992
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let u(g) be the second derivative of 5481*g**6/5 + 7299*g**5/20 - 2111*g**4/3 - 327*g**3/2 + 90*g**2 - 5834*g. Express the second largest root of u(d) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
32
|
math
|
algebra_polynomial_roots_train_0993
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let s be (2 + -6)/(-5 + 148172/29636). Suppose -5863*x**3 + 263*x**3 - 4738*x**2 - s*x**3 + 226*x**2 + 432 + 1958*x**3 + 1332*x - 15400*x**4 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
math
|
algebra_polynomial_roots_train_0994
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let v(h) be the second derivative of 715*h**7/42 - 171*h**6/4 + 1591*h**5/60 + 15*h**4 - 24*h**3 - 26*h**2 - 33*h. Let l(b) be the first derivative of v(b). Suppose l(a) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
algebra_polynomial_roots_train_0995
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let c(z) be the third derivative of 2080*z**7/21 + 105*z**6 - 6*z**5/5 - 189*z**4/4 - 27*z**3 - 123*z**2. Express the second largest root of c(g) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_polynomial_roots_train_0996
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let a be (30/25)/((-180)/(-300)). If 3699/20*x - 2871/10*x**a - 192*x**3 - 567/20 + 480*x**4 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_polynomial_roots_train_0997
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Find the value of n + m, where n/m is the second largest root of -157216/9*q**2 - 640 + 563200/9*q**4 - 20768/3*q + 13760*q**3 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
27
|
math
|
algebra_polynomial_roots_train_0998
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Suppose -72 = 147*f + 140*f - 311*f. Let -27*m + 981*m**2 + 705/7*m**f - 324/7 - 3861*m**4 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14
|
math
|
algebra_polynomial_roots_train_0999
|
algebra_polynomial_roots
| null |
[
{
"role": "user",
"content": "Let y(n) be the first derivative of 1664*n**5 + 1872*n**4 + 19 - 1053/5*n + 546/5*n**3 - 1053/2*n**2. For y(w) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
math
|
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