## Selina Concise Mathematics Class 10 ICSE Solutions Quadratic Equations

APlusTopper.com provides step by step solutions for Selina Concise ICSE Solutions for Class 10 Mathematics Chapter 5 Quadratic Equations. You can download the Selina Concise Mathematics ICSE Solutions for Class 10 with Free PDF download option. Selina Publishers Concise Mathematics for Class 10 ICSE Solutions all questions are solved and explained by expert mathematic teachers as per ICSE board guidelines.

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**Selina ICSE Solutions for Class 10 Maths Chapter 5 Quadratic Equations**

**Exercise 5(A)**

**Question 1.**

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

(i) 7x^{2} – 9x +2 =0

(ii) 6x^{2} – 13x +4 =0

(iii) 25x^{2} – 10x +1=0

(iv) x^{2} + 2√3x – 9=0

(v) x^{2} – ax – b^{2} =0

(vi) 2x^{2} +8x +9=0

**Solution:**

**Question 2(i).**

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

**Solution:**

**Question 2(ii).**

Find the value of ‘p’, if the following quadratic equations have equal roots : x^{2} + (p – 3)x + p = 0

**Solution:**

x^{2} + (p – 3)x + p = 0

Here, a = 1, b = (p – 3), c = p

Since, the roots are equal,

⇒ b^{2}– 4ac = 0

⇒ (p – 3)^{2}– 4(1)(p) = 0

⇒p^{2} + 9 – 6p – 4p = 0

⇒ p^{2}– 10p + 9 = 0

⇒p^{2}-9p – p + 9 = 0

⇒p(p – 9) – 1(p – 9) = 0

⇒ (p -9)(p – 1) = 0

⇒ p – 9 = 0 or p – 1 = 0

⇒ p = 9 or p = 1

**Question 3.**

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

**Solution:**

**Question 4.**

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

**Solution:**

**Question 5.**

Find the value of p for which the equation 3x^{2}– 6x + k = 0 has distinct and real roots.

**Solution:**

**Exercise 5(B)**

**Question 1.**

Solve : x² – 10x – 24 = 0

**Solution:**

**Question 2.**

Solve : x² – 16 = 0

**Solution:**

**Question 3.**

**Solution:**

**Question 4.**

Solve : x(x – 5) = 24

**Solution:**

**Question 5.**

**Solution:**

**Question 6.**

**Solution:**

**Question 7.**

**Solution:**

**Question 8.**

**Solution:**

**Question 9.**

Solve : (2x – 3)² = 49

**Solution:**

**Question 10.**

Solve : 2(x² – 6) = 3(x – 4)

**Solution:**

**Question 11.**

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

**Solution:**

**Question 12.**

Solve : x² – (a + b)x + ab = 0

**Solution:**

**Question 13.**

(x + 3)² – 4(x + 3) – 5 = 0

**Solution:**

**Question 14.**

4(2x – 3)² – (2x – 3) – 14 = 0

**Solution:**

**Question 15.**

**Solution:**

**Question 16.**

2x^{2} – 9x + 10 = 0, When

(i) x∈ N

(ii) x∈ Q

**Solution:**

**Question 17.**

**Solution:**

**Question 18.**

**Solution:**

**Question 19.**

**Solution:**

**Question 20.**

**Solution:**

**Question 21.**

Find the quadratic equation, whose solution set is :

(i) {3, 5} (ii) {-2, 3}

**Solution:**

**Question 22(i).**

**Solution:**

**Question 22(ii).**

**Solution:**

**Question 23.**

Find the value of x, if a + 1=0 and x^{2} + ax – 6 =0.

**Solution:**

**Question 24.**

Find the value of x, if a + 7=0; b + 10=0 and 12x^{2} = ax – b.

**Solution:**

If a + 7 =0, then a = -7

and b + 10 =0, then b = – 10

Put these values of a and b in the given equation

**Question 25.**

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

**Solution:**

**Question 26.**

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

**Solution:**

**Question 27.**

Determine whether x = -1 is a root of the equation x^{2} – 3x +2=0 or not.

**Solution:**

x^{2} – 3x +2=0

Put x = -1 in L.H.S.

L.H.S. = (-1)^{2 }– 3(-1) +2

= 1 +3 +2=6 ≠ R.H.S

Then x = -1 is not the solution of the given equation.

**Question 28.**

If x = 2/3 is a solution of the quadratic equation 7x^{2}+mx – 3=0; Find the value of m.

**Solution:**

**Question 29.**

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

**Solution:**

**Question 30.**

If quadratic equation x^{2} – (m + 1) x + 6=0 has one root as x =3; find the value of m and the root of the equation.

**Solution:**

**Question 31.**

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.

**Solution:**

**Question 32.**

**Solution:**

**Question 33.**

**Solution:**

**Question 34.**

**Solution:**

**Exercise 5(C)**

**Question 1.**

**Solution:**

**Question 2.**

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

(i) x^{2} – 8x+5=0

(ii) 5x^{2} +10x – 3 =0

**Solution:**

**Question 3(i).**

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

(i) 2x^{2} – 10x +5=0

**Solution:**

**Question 3(ii).**

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

**Solution:**

**Question 3(iii).**

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

x^{2} – 3x – 9 =0

**Solution:**

**Question 3(iv).**

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

**Solution:**

**Question 4.**

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

(i) 3x^{2} – 12x – 1 =0

(ii) x^{2} – 16 x +6= 0

(iii) 2x^{2} + 11x + 4= 0

**Solution:**

**Question 5.**

Solve:

(i) x^{4} – 2x^{2} – 3 =0

(ii) x^{4} – 10x^{2} +9 =0

**Solution:**

**Question 6.**

Solve :

(i) (x^{2} – x)^{2} + 5(x^{2} – x)+ 4=0

(ii) (x^{2} – 3x)^{2} – 16(x^{2} – 3x) – 36 =0

**Solution:**

**Question 7.**

**Solution:**

**Question 8.**

**Solution:**

**Question 9.**

Solve the following equation and give your answer correct to 3 significant figures:

5x² – 3x – 4 = 0

**Solution:**

**Question 10.**

Solve for x using the quadratic formula. Write your answer correct to two significant figures.

(x – 1)^{2} – 3x + 4 = 0

**Solution:**

**Exercise 5(D)**

**Question 1.**

**Solution:**

**Question 2.**

Solve: (2x+3)^{2}=81

**Solution:**

**Question 3.**

Solve: a²x² – b² = 0

**Solution:**

**Question 4.**

**Solution:**

**Question 5.**

**Solution:**

**Question 6.**

Solve: 2x^{4} – 5x² + 3 = 0

**Solution:**

**Question 7.**

Solve: x^{4} – 2x² – 3 = 0.

**Solution:**

**Question 8.**

**Solution:**

**Question 9.**

**Solution:**

**Question 10.**

**Solution:**

**Question 11.**

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

**Solution:**

**Question 12.**

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

(i) x^{2} – 5x -10=0 (ii) 3x^{2} – x – 7 =0

**Solution:**

**Question 13.**

**Solution:**

**Question 14.**

Solve :

(i) x^{2} – 11x – 12 =0; when x ∈ N

(ii) x^{2} – 4x – 12 =0; when x ∈ I

(iii) 2x^{2} – 9x + 10 =0; when x ∈ Q

**Solution:**

**Question 15.**

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

**Solution:**

**Question 16.**

**Solution:**

**Question 17.**

**Solution:**

**Question 18.**

**Solution:**

**Question 19.**

**Solution:**

**Question 20.**

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

x² + 2(m – 1)x + (m + 5) = 0

**Solution:**

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