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# S Chand ICSE Maths Solutions Class 10 Chapter 3 Quadratic Equations Exercise 5A

Hi students, Welcome to Amans Maths Blogs (AMB). In this post, you will get S Chand ICSE Maths Solutions Class 10 Chapter 3 Quadratic Equations Exercise 5A. This is the chapter of introduction of ‘Quadratic Equations‘ included in ICSE 2021 Class 10 Maths syllabus.

## S Chand ICSE Maths Solutions Class 10 Chapter 5 Quadratic Equations Exercise 5A

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 1

(i) (x – 3)(x + 7) = 0

(ii) (x – 3)(x + 7) = 0

S Chand ICSE Maths Solutions:

(x – 3)(x + 7) = 0 ⇒ x – 3 = 0 or x + 7 = 0 ⇒ x = 3 or x = -7.

(3x + 4)(2x – 11) = 0 ⇒ 3x + 4 = 0 or 2x – 11 = 0 ⇒ x = -4/3 or x = 11/2.

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 2

x2 = 4x

S Chand ICSE Maths Solutions:

x2 = 4x

⇒ (x2 – 4x) = 0

⇒ x(x – 4) = 0

⇒ x = 0 or x – 4 = 0

⇒ x = 0 or x = 4

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 3

(x/3 – 1)(x/2 + 7) = 0

S Chand ICSE Maths Solutions:

(x/3 – 1)(x/2 + 7) = 0

⇒ x/3 – 1 = 0 or x/2 + 7 = 0

⇒ x/3 = 1 or x/2 = -7

⇒ x = 3 or x = -14

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 4

(x2 – 5x) / 2 = 0

S Chand ICSE Maths Solutions:

(x2 – 5x) / 2 = 0

⇒ (x2 – 5x) = 0

⇒ x(x – 5) = 0

⇒ x = 0 or x – 5 = 0

⇒ x = 0 or 5

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 5

x2 – 3x – 10 = 0

S Chand ICSE Maths Solutions:

x2 – 3x – 10 = 0

⇒ x2 – 5x + 2x – 10 = 0

⇒ x(x – 5) + 2(x – 5) = 0

⇒ (x – 5)(x + 2) = 0

⇒ x = 5 or -2

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 6

x2 + x – 12 = 0

S Chand ICSE Maths Solutions:

x2 + x – 12 = 0

⇒ x2 + 4x – 3x – 12 = 0

⇒ x(x + 4) – 3(x + 4) = 0

⇒ (x + 4)(x – 3) = 0

⇒ x = -4 or 3

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 7

2(x2 + 1) = 5x

S Chand ICSE Maths Solutions:

2(x2 + 1) = 5x

⇒ 2x2 – 5x + 2 = 0

⇒ 2x2 – 4x – x + 2 = 0

⇒ 2x(x – 2) – 1(x – 2) = 0

⇒ (x – 2)(2x – 1) = 0

⇒ x = 2 or 1/2

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 8

x(2x + 5) = 3

S Chand ICSE Maths Solutions:

x(2x + 5) = 3

⇒ 2x2 + 5x – 3 = 0

⇒ 2x2 + 6x – x – 3 = 0

⇒ 2x(x + 3) – 1(x + 3) = 0

⇒ (x + 3)(2x – 1) = 0

⇒ x + 3 = 0 or 2x – 1 = 0

⇒ x = -3 or 1/2

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 9

4x2 – 3x – 1 = 0

S Chand ICSE Maths Solutions:

4x2 – 3x – 1 = 0

⇒ 4x2 – 4x + x – 1 = 0

⇒ 4x(x – 1) + 1(x – 1) = 0

⇒ (x – 1)(4x + 1) = 0

⇒ x – 1 = 0 or 4x – 1 = 0

⇒ x = 1 or 1/4

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 10

6x2 – 13x + 5 = 0

S Chand ICSE Maths Solutions:

6x2 – 13x + 5 = 0

⇒ 6x2 – 10x – 3x + 5 = 0

⇒ 2x(3x – 5) – 1(3x – 5) = 0

⇒ (3x – 5)(2x – 1) = 0

⇒ 3x – 5 = 0 or 2x – 1 = 0

⇒ x = 5/3 or 1/2

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 11

3x2 – 5x – 12 = 0

S Chand ICSE Maths Solutions:

3x2 – 5x – 12 = 0

⇒ 3x2 – 9x + 4x – 12 = 0

⇒ 3x(x – 3) + 4(x – 3) = 0

⇒ (x – 3)(3x + 4) = 0

⇒ x – 3 = 0 or 3x + 4 = 0

⇒ x = 3 or -4/3

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 12

2x2 – 11x + 5 = 0

S Chand ICSE Maths Solutions:

2x2 – 11x + 5 = 0

⇒ 2x2 – 10x – x + 5 = 0

⇒ 2x(x – 5) – 1(x – 5) = 0

⇒ (x – 5)(2x – 1) = 0

⇒ x – 5 = 0 or 2x – 1 = 0

⇒ x = 5 or 1/2

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 13

x/2 + 6/x = 4

S Chand ICSE Maths Solutions:

x/2 + 6/x = 4

⇒ (x2 + 12)/2x = 4

⇒ x2 – 8x + 12 = 0

⇒ x2 – 6x – 2x + 12 = 0

⇒ x(x – 6) – 2(x – 6) = 0

⇒ (x – 6)(x – 2) = 0

⇒ x – 6 = 0 or x – 2 = 0

⇒ x = 6 or 2.

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 14

10x – 1/x = 3

S Chand ICSE Maths Solutions:

10x – 1/x = 3

⇒ 10x2 – 1 = 3x

⇒ 10x2 – 3x – 1 = 0

⇒ 10x2 – 5x + 2x – 1 = 0

⇒ 5x(2x – 1) + 1(2x – 1) = 0

⇒ (2x – 1)(5x + 1) = 0

⇒ 2x – 1 = 0 or 5x + 1 = 0

⇒ x = 1/2 or -1/5

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 15

9x + 1/x = 6

S Chand ICSE Maths Solutions:

9x + 1/x = 6

⇒ 9x2 + 1 = 6x

⇒ 9x2 – 6x + 1 = 0

⇒ (3x)2 – 2(3x)(1) + 1 = 0

⇒ (3x – 1)2 = 0

⇒ (3x – 1)(3x – 1) = 0

⇒ (3x – 1) = 0 or (3x – 1) = 0

⇒ x = 1/3 or 1/3

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 16

x/5 + 28/(x + 2) = 5

S Chand ICSE Maths Solutions:

⇒ [x(x + 2) + 140] / 5(x + 2) = 5

⇒ x2 + 2x + 140 = 25(x + 2)

⇒ x2 + 2x + 140 = 25x + 50

⇒ x2 + 2x – 25x + 140 – 50 = 0

⇒ x2 – 23x + 90 = 0

⇒ x2 – 18x – 5x + 90 = 0

⇒ x(x – 18) – 5(x – 18) = 0

⇒ (x – 18)(x – 5) = 0

⇒ (x – 18) = 0 or (x – 5) = 0

⇒ x = 18 or x = 5

⇒ x = 18 or 5

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 17

x/(x – 1) + (x – 1)/x = 2 1/2

S Chand ICSE Maths Solutions:

x/(x – 1) + (x – 1)/x = 2 1/2

⇒ [x2 + (x – 1)2] / x(x – 1) = 5/2

⇒ 2[x2 + x2 – 2x + 1]   = 5x(x – 1)

⇒ 4x2 – 4x + 2   = 5x2 – 5x

⇒ x2 – x – 2 = 0

⇒ x2 – 2x + x – 2 = 0

⇒ x(x – 2) + 1(x – 2) = 0

⇒ (x + 1)(x – 2) = 0

⇒ (x + 1) = 0 or (x – 2) = 0

⇒ x = -1 or 2

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 18

x/a – (a + b)/x = b(a + b)/ax

S Chand ICSE Maths Solutions:

x/a – (a + b)/x = b(a + b)/ax

⇒ [x2 – a(a + b)]/ax = b(a + b)/ax

⇒ x2 – a(a + b) = b(a + b)

⇒ x2 – a(a + b) – b(a + b) = 0

⇒ x2 – (a + b)2 = 0

⇒ [x + (a + b)][x – (a + b)] = 0

⇒ [x + (a + b)] = 0 or [x – (a + b)] = 0

⇒ x = (a + b) or -(a + b)

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 19

1/(a + b + x) – 1/x = 1/a + 1/b

S Chand ICSE Maths Solutions:

1/(a + b + x) – 1/x = 1/a + 1/b

⇒ (x – a – b – x)/x(a + b + x) = (a + b)/ab

⇒ -(a + b)/x(a + b + x) = (a + b)/ab

⇒ -1/x(a + b + x) = 1/ab

⇒ -x(a + b + x) = ab

⇒ -x2 – ax – bx – ab = 0

⇒ x2 + ax + bx + ab = 0

⇒ x(x + a) + b(x + a) = 0

⇒ (x + a)(x + b) = 0

⇒ (x + a) = 0 or (x + b) = 0

⇒ x = -a or -b

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 20

(x + 3)/(x – 2) – (1 – x)/x = 17/4, x ≠ 0, 2.

S Chand ICSE Maths Solutions:

(x + 3)/(x – 2) – (1 – x)/x = 17/4

⇒ [x(x + 3) – (x – 2)(1 – x)] / x(x – 2) = 17/4

⇒ [x2 + 3x – x + x2 + 2 – 2x] / (x2 – 2x) = 17/4

⇒ 4[2x2 + 2]  = 17(x2 – 2x)

⇒ 8x2 + 8  = 17x2 – 34x

⇒ 17x2 – 8x– 34x – 8 = 0

⇒ 9x– 34x – 8 = 0

⇒ 9x– 36x + 2x – 8 = 0

⇒ 9x(x – 4) + 2(x – 4) = 0

⇒ (x – 4)(9x + 2) = 0

⇒ (x – 4) = 0 or (9x + 2) = 0

⇒ x = 4 or -2/9

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 21

2x/(x – 4) + (2x – 5)/(x – 3) = 25/3

S Chand ICSE Maths Solutions:

2x/(x – 4) + (2x – 5)/(x – 3) = 25/3

⇒ [2x(x – 3) + (2x – 5)(x – 4)] / (x – 4)(x – 3) = 25/3

⇒ [2x2 – 6x + 2x2 – 8x – 5x + 20] / (x2 – 7x + 12) = 25/3

⇒ 3[4x2 – 19x + 20] = 25(x2 – 7x + 12)

⇒ 12x2 – 57x + 60 = 25x2 – 175x + 300

⇒  25x2 – 12x2 – 175x + 57x + 300 – 60 = 0

⇒  13x2 – 118x + 240 = 0

⇒  13x2 – 78x – 40x + 240 = 0

⇒  13x(x – 6) – 40(x – 6) = 0

⇒  (x – 6)(13x – 40) = 0

⇒  (x – 6) = 0 or (13x – 40) = 0

⇒  x = 6 or 40/13

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 22

(x + 1)/(x – 1) – (x – 1)/(x + 1) = 5/6, x ≠ 1, -1.

S Chand ICSE Maths Solutions:

(x + 1)/(x – 1) – (x – 1)/(x + 1) = 5/6

⇒ [(x + 1)2 – (x – 1)2] / (x – 1)(x + 1) = 5/6

⇒ 6[x2 + 2x + 1 – x2 +2x – 1] = 5(x2 – 1)

⇒ 6[4x] = 5(x2 – 1)

⇒ 5x2 – 24x – 5 = 0

⇒ 5x2 – 25x + x – 5 = 0

⇒ 5x(x – 5) + 1(x – 5) = 0

⇒ (5x + 1)(x – 5) = 0

⇒ (5x + 1) = 0 or (x – 5) = 0

⇒ x = -1/5 or 5

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 23

√2x2 – 3x – 2√2 = 0

S Chand ICSE Maths Solutions:

√2x2 – 3x – 2√2 = 0

⇒ √2x2 – 4x + x – 2√2 = 0

⇒ √2x(x – 2√2) + 1(x – 2√2) = 0

⇒ (√2x + 1)(x – 2√2) = 0

⇒ (√2x + 1) = 0 or (x – 2√2) = 0

⇒ x = -1/√2 or 2√2

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 24

a(x2 + 1) – x(a2 + 1) = 0

S Chand ICSE Maths Solutions:

a(x2 + 1) – x(a2 + 1) = 0

⇒ ax2 + a – xa2 – x = 0

⇒ ax2 – xa2 – x + a = 0

⇒ ax(x – a) – 1(x – a) = 0

⇒ (ax – 1)(x – a) = 0

⇒ (ax – 1) = 0 or (x – a) = 0

⇒ x = 1/a or a

S Chand ICSE Solutions Class 10 Maths Quadratic Equations Exercise 5A: Ques No 25

Find the solution set of {x : x2 – 2x – 35 = 0}

S Chand ICSE Maths Solutions:

x2 – 2x – 35 = 0

⇒ x2 – 7x + 5x – 35 = 0

⇒ x(x – 7) + 5(x – 7) = 0

⇒ (x + 5)(x – 7) = 0

⇒ (x + 5) = 0 or (x – 7) = 0

⇒ x = -5 or 7

⇒ x ∈ {-5, 7}

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