If $a, b, c$ are in GP, then the equations $ax^2+2bx+c=0$ and $dx^2+2ex+f=0$ have a common root if $\frac{d}{a}, \frac{e}{b}, \frac{f}{c}$ are in...
36331
One root common to $ax^2+2bx+c=0$ and $dx^2+2ex+f=0$
64754
Find $x$ in the equation $ax^3+bx^2+cx=d$
154393
Roots of polynomial with real coefficients appear in conjugate pairs.
18702
If $ax^2+(c+b)x+e+d=0$ has real roots greater than $1$, show that $ax^4+bx^3+cx^2+dx+e$ has at least one real root
64448
Find a quadratic equation with root $x_1^2$ and $x_2^2$
140481
How to tell if a quartic equation has a multiple root.
44250
rational number solutions to $\frac{a}{a^2+1} + \frac{b}{b^2+1} = \frac{c}{c^2+1}$ with $abc\ne 0$
141093
How many real roots does $(x-a)^3+(x-b)^3+(x-c)^3$ have?
44020
Probability of $x^2+bx+c=0$ having real roots
15626
Relations of a~b iff b = ak^2
111847
For $a,b,c>0$, prove that $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge a+b+c+\frac{4(a-b)^2}{a+b+c}$
63689
proving roots of equation $x^2+x+4f=0$ are real.
137048
If $p, q, r$ are the roots of $x^3 -x+1=0$, what is $p^5 + q^5 + r^5$?
72410
If $\alpha_1,\alpha_2,\ldots,\alpha_n$ be the roots of the equation $x^n+1$
118266
If $f^2(b) - f^2(a) = b^2 - a^2$, then the equation $f'(x)f(x) = x$ has at least one root in (a, b).
55197
Roots of $ x^3-3x+1$
33469
Diophantine equation $ax + by = c$ has an integer solution $x_0, y_0$ if and only if $\gcd(a,b)|c$