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# Selina solutions for Class 10 Maths chapter 5 - Quadratic Equations

#### Selina Selina ICSE Concise Mathematics Class 10

Exercise 5(A)Exercise 5(B)Exercise 5(C)Exercise 5(D)Exercise 5(E)Exercise 5(F)

#### Selina solutions for Class 10 Maths Chapter 5 Exercise Exercise 5(A) [Page 54]

Exercise 5(A) | Q 1.1 | Page 54

Find which of the following equation are quadratic:

(3x - 1)2 = 5(x + 8)

Exercise 5(A) | Q 1.2 | Page 54

Find which of the following equation are quadratic:

5x2 - 8x = -3(7 - 2x)

Exercise 5(A) | Q 1.3 | Page 54

Find which of the following equation are quadratic:

(x - 4)(3x + 1) = (3x - 1)(x +2)

Exercise 5(A) | Q 1.4 | Page 54

Find which of the following equation are quadratic:

x2 + 5x - 5 = (x - 3)2

Exercise 5(A) | Q 1.5 | Page 54

Find which of the following equations are quadratic:

7x3 - 2x2 + 10 = (2x - 5)2

Exercise 5(A) | Q 1.6 | Page 54

Find which of the following equation are quadratic:

(x - 1)2 + (x + 2)2 + 3(x +1) = 0

Exercise 5(A) | Q 2.1 | Page 54

Is x = 5 a solution of the quadratic equation x2 - 2x - 15 = 0?

Exercise 5(A) | Q 2.2 | Page 54

Is x = -3 a solution of the quadratic equation 2x2 - 7x + 9 = 0?

Exercise 5(A) | Q 3 | Page 54

If sqrt (2/3) is a solution of equation 3x2 + mx + 2 = 0, find the value of m.

Exercise 5(A) | Q 4 | Page 54

2/3and 1 are the solutions of equation mx2 + nx + 6 = 0. Find the values of m and n.

Exercise 5(A) | Q 5 | Page 54

If 3 and -3 are the solutions of equation ax2 + bx - 9 = 0. Find the values of a and b.

#### Selina solutions for Class 10 Maths Chapter 5 Exercise Exercise 5(B) [Page 56]

Exercise 5(B) | Q 1.1 | Page 56

Without solving comment upon the nature of roots of each of the following equations:

7x2 – 9x + 2 = 0

Exercise 5(B) | Q 1.2 | Page 56

Without solving comment upon the nature of roots of each of the following equations:

6x2 – 13x + 4 = 0

Exercise 5(B) | Q 1.3 | Page 56

Without solving comment upon the nature of roots of each of the following equations:

25x^2 − 10x + 1 = 0

Exercise 5(B) | Q 1.4 | Page 56

Without solving comment upon the nature of roots of each of the following equations : "x"^2+2sqrt3"x"-9=0

Exercise 5(B) | Q 1.5 | Page 56

Without solving comment upon the nature of roots of each of the following equations:

"x"^2 – "ax" – "b"^2 = 0

Exercise 5(B) | Q 1.6 | Page 56

Without solving comment upon the nature of roots of each of the following equations:

2"x"^2 + 8"x" + 9 = 0

Exercise 5(B) | Q 2.1 | Page 56

Find the value of p, if the following quadratic equation has equal roots: 4x2 – (p – 2)x + 1 = 0

Exercise 5(B) | Q 2.2 | Page 56

Find the value of 'p', if the following quadratic equations have equal roots :

x2 + (p - 3)x + p = 0

Exercise 5(B) | Q 3 | Page 56

The equation 3x^2 – 12x + (n – 5) = 0 has equal roots. Find the value of n.

Exercise 5(B) | Q 4 | Page 56

Find the value of m, if the following equation has equal roots : (m – 2)x2 – (5+m)x +16 =0

Exercise 5(B) | Q 5 | Page 56

Find the value of k for which the equation 3x2- 6x + k = 0 has distinct and real roots.

#### Selina solutions for Class 10 Maths Chapter 5 Exercise Exercise 5(C) [Pages 59 - 60]

Exercise 5(C) | Q 1 | Page 59

Solve equation using factorisation method:

x2 - 10x - 24 = 0

Exercise 5(C) | Q 2 | Page 59

Solve equation using factorisation method:

x2 - 16 = 0

Exercise 5(C) | Q 3 | Page 59

Solve equation using factorisation method:

2"x"^2 = 1/2"x" = 0

Exercise 5(C) | Q 4 | Page 59

Solve equation using factorisation method:

x (x - 5) = 24

Exercise 5(C) | Q 5 | Page 59

Solve equation using factorisation method:

9/5"x" = 5 + "x"^2

Exercise 5(C) | Q 6 | Page 59

Solve equation using factorisation method:

6/"x" = 1 + "x"

Exercise 5(C) | Q 7 | Page 59

Solve equation using factorisation method:

x = (3"x" + 1)/(4"x")

Exercise 5(C) | Q 8 | Page 59

Solve equation using factorisation method:

x + 1/"x" = 2.5

Exercise 5(C) | Q 9 | Page 59

Solve equation using factorisation method:

(2x - 3)2 = 49

Exercise 5(C) | Q 10 | Page 59

Solve equation using factorisation method:

2(x2 - 6) = 3(x - 4)

Exercise 5(C) | Q 11 | Page 59

Solve equation using factorisation method:

(x +1)(2x + 8) = (x + 7)(x +3)

Exercise 5(C) | Q 12 | Page 59

Solve equation using factorisation method:

x2 - (a + b) x + ab = 0

Exercise 5(C) | Q 13 | Page 59

Solve equation using factorisation method:

(x - 3)2 -4(x +3) -5 = 0

Exercise 5(C) | Q 14 | Page 59

Solve equation using factorisation method:

4(2x - 3)2 - (2x - 3) - 14 = 0

Exercise 5(C) | Q 15 | Page 59

Solve equation using factorisation method:

(3"x" -2)/(2"x" -3) = (3"x" - 8)/("x" + 4)

Exercise 5(C) | Q 16 | Page 59

Solve equation using factorisation method:

2x2 - 9x + 10 = 0, When

(i) x∈ N

(ii) x∈ Q

Exercise 5(C) | Q 17 | Page 59

Solve equation using factorisation method:

("x" - 3)/("x" + 3) + ("x" + 3)/("x" - 3) = 2 1/2

Exercise 5(C) | Q 18 | Page 59

Solve equation using factorisation method:

4/("x" + 2) - 1/("x" + 3) = 4/(2"x" + 1)

Exercise 5(C) | Q 19 | Page 59

Solve equation using factorisation method:

5/("x" -2) - 3/("x" + 6) = 4/"x"

Exercise 5(C) | Q 21.1 | Page 59

Find the quadratic equation, whose solution set is :

{3,5}

Exercise 5(C) | Q 21.2 | Page 59

Find the quadratic equation, whose solution set is :

(-2,3}

Exercise 5(C) | Q 22.1 | Page 59

Solve:

"x"/3 + 3/(6 - "x") = (2(6 +"x"))/15; (x ≠ 6)

Exercise 5(C) | Q 22.2 | Page 59

Solve the equation 9x^2 + (3x)/4 + 2 = 0 if possible for real values of x

Exercise 5(C) | Q 23 | Page 60

Find the value of x, if a + 1=0 and x2 + ax - 6 =0.

Exercise 5(C) | Q 24 | Page 60

Find the value of x, if a + 7=0; b + 10=0 and 12x2 = ax - b.

Exercise 5(C) | Q 25 | Page 60

Use the substitution y= 2x +3 to solve for x, if 4(2x+3)2 – (2x+3) – 14 =0.

Exercise 5(C) | Q 26 | Page 60

Without solving the quadratic equation 6x2 – x – 2=0, find whether x = 2/3 is a solution of this equation or not.

Exercise 5(C) | Q 27 | Page 59

Determine whether x = -1 is a root of the equation x2 - 3x +2=0 or not.

Exercise 5(C) | Q 28 | Page 60

If x = 2/3 is a solution of the quadratic equation 7x2+mx - 3=0;

Find the value of m.

Exercise 5(C) | Q 29 | Page 60

If x = -3 and x = 2/3 are solutions of quadratic equation mx+ 7x + n = 0, find the values of m and n.

Exercise 5(C) | Q 30 | Page 60

If quadratic equation x2 - (m + 1) x + 6=0 has one root as x =3;

find the value of m and the root of the equation.

Exercise 5(C) | Q 31 | Page 60

Given that 2 is a root of the equation 3x² – p(x + 1) = 0 and that the equation px² – qx + 9 = 0 has equal roots, find the values of p and q.

Exercise 5(C) | Q 32 | Page 60

Solve : "x"/"a" - ("a" + "b")/"x" = ("b"("a" + "b"))/"ax"

Exercise 5(C) | Q 33 | Page 60

Solve : (1200/"x" + 2)(x - 10) - 1200 = 60

Exercise 5(C) | Q 34 | Page 60

If -1 and 3 are the roots of x2+px+q=0
then find the values of p and q

#### Selina solutions for Class 10 Maths Chapter 5 Exercise Exercise 5(D) [Page 64]

Exercise 5(D) | Q 1.01 | Page 64

Solve the following equation using the formula

x^2 - 6x = 27

Exercise 5(D) | Q 1.02 | Page 64

Solve the following equation using the formula

x^2 + 10x + 21 = 0

Exercise 5(D) | Q 1.03 | Page 64

Solve each of the following equations using the formula:

x^2 + 6x – 10 = 0

Exercise 5(D) | Q 1.04 | Page 64

Solve each of the following equations using the formula:

x^2 + 2x – 6 = 0

Exercise 5(D) | Q 1.05 | Page 64

Solve each of the following equations using the formula:

3x^2 + 2x – 1 = 0

Exercise 5(D) | Q 1.06 | Page 64

Solve the following equations using the formula

2x^2 + 7x + 5 = 0

Exercise 5(D) | Q 1.07 | Page 64

Solve each of the following equations using the formula:

2/3x=-1/6x^2-1/3

Exercise 5(D) | Q 1.08 | Page 64

Solve each of the following equations using the formula:

1/15x^2+5/3=2/3x

Exercise 5(D) | Q 1.09 | Page 64

Solve each of the following equations using the formula:

x^2-6=2sqrt2x

Exercise 5(D) | Q 1.1 | Page 64

Solve each of the following equations using the formula:

4/x-3=5/(2x+3)

Exercise 5(D) | Q 1.11 | Page 64

Solve each of the following equations using the formula :

(2x+3)/(x+3)=(x+4)/(x+2)

Exercise 5(D) | Q 1.12 | Page 64

Solve each of the following equations using the formula:

sqrt6x^2-4x-2sqrt6=0

Exercise 5(D) | Q 1.13 | Page 64

Solve each of the following equations using the formula:

(2x)/(x-4)+(2x-5)/(x-3)=8 1/3

Exercise 5(D) | Q 1.14 | Page 64

Solve each of the following equations using the formula:

(x-1)/(x-2)+(x-3)/(x-4)=3 1/3

Exercise 5(D) | Q 2.1 | Page 64

Solve the following equations for x and give, in each case, your answer correct to one decimal place :

x2 – 8x+5=0

Exercise 5(D) | Q 2.2 | Page 64

Solve the following equations for x and give, in given case, your answer correct to one decimal place :

5x2 +10x – 3 =0

Exercise 5(D) | Q 3.1 | Page 64

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :

2x2 – 10x +5=0

Exercise 5(D) | Q 3.2 | Page 64

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :
4x + 6/x + 13 = 0

Exercise 5(D) | Q 3.4 | Page 64

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :

x2 – 3x – 9 =0

Exercise 5(D) | Q 3.5 | Page 64

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :

x^2 - 5x - 10 = 0

Exercise 5(D) | Q 4.1 | Page 64

Solve the following equations for x and give, in each case, your answer correct to 3 decimal places

3x2 – 12x – 1 =0

Exercise 5(D) | Q 4.2 | Page 64

Solve each of the following equations for x and give, in each case, your answer correct to 3 decimal places :

x2 - 16 x +6= 0

Exercise 5(D) | Q 4.3 | Page 64

Solve the following equations for x and give, in each case, your answer correct to 3 decimal places

2x2 + 11x + 4= 0

Exercise 5(D) | Q 5.1 | Page 64

Solve :

x4 - 2x2 - 3 = 0

Exercise 5(D) | Q 5.2 | Page 64

Solve : x4 - 10x2 +9 =0

Exercise 5(D) | Q 6.1 | Page 64

Solve : (x2 – x)2 + 5(x2 – x)+ 4=0

Exercise 5(D) | Q 6.2 | Page 64

Solve :

(x2 - 3x)2 - 16(x2 - 3x) - 36 =0

Exercise 5(D) | Q 7.1 | Page 64

Solve:

sqrt("x"/("x" -3)) + sqrt(("x" -3)/"x") = 5/2

Exercise 5(D) | Q 7.2 | Page 64

Solve:

((2"x" -3)/("x" -1)) - 4(("x" - 1)/(2"x" - 3)) = 3

Exercise 5(D) | Q 7.3 | Page 64

Solve:

((3x + 1)/(x + 1)) + ((x + 1)/(3x + 1)) = 5/2

Exercise 5(D) | Q 8 | Page 64

Solve the equation 2x - 1/x = 7.Write your answer correct to two decimal places.

Exercise 5(D) | Q 9 | Page 64

Solve the following equation and give your answer correct to 3 significant figures: 5x² – 3x – 4 = 0

Exercise 5(D) | Q 10 | Page 64

(x – 1)2 – 3x + 4 = 0

Exercise 5(D) | Q 11 | Page 64

Solve the quadratic equation x2 -  3(x + 3) = 0; Give your answer correct two significant figures

#### Selina solutions for Class 10 Maths Chapter 5 Exercise Exercise 5(E) [Pages 66 - 67]

Exercise 5(E) | Q 1 | Page 66

Solve (2x)/(x - 3) + 1/(2x + 3) + (3x + 9)/((x - 3)(2x +3)) = 0; x != 3, x != - 3/2

Exercise 5(E) | Q 2 | Page 66

Solve: (2x+3)= 81

Exercise 5(E) | Q 3 | Page 66

Solve a^2x^2 - b^2 = 0

Exercise 5(E) | Q 3 | Page 67

One root of the quadratic equation x^2 + (3 - 2a)x - 6a = 0 is -3, find its other root.

Exercise 5(E) | Q 4 | Page 66

Solve x^2 - 11/4 x + 15/8 = 0

Exercise 5(E) | Q 5 | Page 66

Solve x + 4/x = -4; x != 0

Exercise 5(E) | Q 6 | Page 66

Solve: 2x4 – 5x² + 3 = 0

Exercise 5(E) | Q 7 | Page 66

Solve: x4 – 2x² – 3 = 0.

Exercise 5(E) | Q 8 | Page 66

Solve 9(x^2 + 1/x^2) - 9(x - 1/x) - 52 = 0

Exercise 5(E) | Q 9 | Page 66

Solve 2(x^2 + 1/x^2) - (x + 1/x) = 11

Exercise 5(E) | Q 11 | Page 66

Solve : (x² + 5x + 4)(x² + 5x + 6) = 120

Exercise 5(E) | Q 12.2 | Page 67

Solve of the following equations, giving answer upto two decimal places.

3x2 – x – 7 =0

Exercise 5(E) | Q 13 | Page 67

Solve (x/(x + 2))^2 - 7(x/(x + 2)) + 12 = 0; x != -2

Exercise 5(E) | Q 14.1 | Page 67

Solve : x2 – 11x – 12 =0; when x ∈ N

Exercise 5(E) | Q 14.2 | Page 67

Solve x2 – 4x – 12 =0; when x ∈ I

Exercise 5(E) | Q 14.3 | Page 67

Solve  2x2 – 9x + 10 =0; when x ∈ Q

Exercise 5(E) | Q 15 | Page 67

Solve : (a + b)²x² – (a + b)x – 6 = 0; a + b ≠ 0

Exercise 5(E) | Q 16 | Page 67

Solve 1/p + 1/q + 1/x = 1/(x + p + q)

Exercise 5(E) | Q 17.1 | Page 67

Solve x(x + 1) + (x + 2)(x + 3) = 42

Exercise 5(E) | Q 17.2 | Page 67

Solve 1/(x - 1) - 2/(x + 2) = 3/(x + 3) - 4/(x + 4)

Exercise 5(E) | Q 18.1 | Page 67

For each equation given below find the values of m so that the equation has equal roots. Also find the solution of equation

(m - 3)x^2 - 4x + 1 = 0

Exercise 5(E) | Q 18.2 | Page 67

For each equation given below find the values of m so that the equation has equal roots. Also find the solution of equation

3x^2 + 12x + (m + 7) = 0

Exercise 5(E) | Q 18.3 | Page 67

For each equation given below find the values of m so that the equation has equal roots. Also find the solution of equation

x^2 - (m + 2)x + (m + 5) = 0

Exercise 5(E) | Q 19 | Page 67

Without solving the following quadratic equation Find the value of p for which the roots are equal

px^2 - 4x + 3 = 0

Exercise 5(E) | Q 20 | Page 67

Without solving the following quadratic equation, find the value of m for which the given equation has equation has real and equal roots.

x^2 + 2(m - 1)x + (m + 5) = 0

#### Selina solutions for Class 10 Maths Chapter 5 Exercise Exercise 5(F) [Page 67]

Exercise 5(F) | Q 1.1 | Page 67

Solve :
(x+5)(x-5)=24

Exercise 5(F) | Q 1.2 | Page 67

Solve :
3x^2 - 2sqrt6x + 2 = 0

Exercise 5(F) | Q 1.3 | Page 67

Solve :
3sqrt(2x^2) - 5x - sqrt2 = 0

Exercise 5(F) | Q 1.4 | Page 67

Solve :
2x - 3 = sqrt(2x^2 - 2x + 21)

Exercise 5(F) | Q 2 | Page 67

One root of the quadratic equation 8x^2 + mx + 15 = 0  is 3/4  Find the value of m. Also, find the other root of the equation.

Exercise 5(F) | Q 4 | Page 67

If p -15 = 0 and  2x^2 + px + 25 = 0;find the values of x.

Exercise 5(F) | Q 5 | Page 67

Find the solution of the equation 2x^2 - mx - 25n = 0 if m + 5 = 0 and n - 1 = 0

Exercise 5(F) | Q 6 | Page 67

If m and n are roots of the equation 1/x - 1/(x - 2) = 3 where x ≠ 0 and x ≠ 2; find m × n.

Exercise 5(F) | Q 7 | Page 67

Solve, using formula :
x^2 + x - (a + 2) (a + 1) = 0

Exercise 5(F) | Q 8 | Page 67

Solve the quadratic equation 8x^2 - 14x + 3 = 0

(i) When "x" in "I(integers)

(ii) When "x" in "Q"(rational numbers)

Exercise 5(F) | Q 9 | Page 67

Find the value of m for which the equation (m + 4)x^2 + ( m + 1)x + 1 = 0  has real and equal roots.

Exercise 5(F) | Q 10 | Page 67

Find the values of m for which equation 3x^2 + mx + 2 = 0 has equal roots. Also, find the roots of the given equation.

Exercise 5(F) | Q 11 | Page 67

Find the value of k for which equation 4x^2 + 8x - k = 0 has real roots.

Exercise 5(F) | Q 12.1 | Page 67

Find, using quadratic formula, the roots of the following quadratic equations, if they exist
3x^2 - 5x + 2 = 0

Exercise 5(F) | Q 12.2 | Page 67

Find, using quadratic formula, the roots of the following quadratic equations, if they exist
x^2 + 4x + 5 = 0

Exercise 5(F) | Q 13.1 | Page 67

Solve : 1/(18 - x) - 1/(18 + x) = 1/24 and x > 0.

Exercise 5(F) | Q 13.2 | Page 67

Solve : ( x - 10) (1200/x + 2) = 1260 and x < 0.

Exercise 5(A)Exercise 5(B)Exercise 5(C)Exercise 5(D)Exercise 5(E)Exercise 5(F)

## Selina solutions for Class 10 Mathematics chapter 5 - Quadratic Equations

Selina solutions for Class 10 Maths chapter 5 (Quadratic Equations) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Selina ICSE Concise Mathematics for Class 10 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Selina textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10 Mathematics chapter 5 Quadratic Equations are Quadratic Equations, Solutions of Quadratic Equations by Factorization, Nature of Roots.

Using Selina Class 10 solutions Quadratic Equations exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Selina Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 10 prefer Selina Textbook Solutions to score more in exam.

Get the free view of chapter 5 Quadratic Equations Class 10 extra questions for Maths and can use Shaalaa.com to keep it handy for your exam preparation

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