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

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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.

Ques No 2

x² = 4x

Solutions:

x² = 4x

⇒ (x² – 4x) = 0

⇒ x(x – 4) = 0

⇒ x = 0 or x – 4 = 0

⇒ x = 0 or x = 4 

Exercise 5A: Ques No 3

(x/3 – 1)(x/2 + 7) = 0

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 

Ques No 4

(x² – 5x) / 2 = 0

Solutions:

(x² – 5x) / 2 = 0

⇒ (x² – 5x) = 0

⇒ x(x – 5) = 0

⇒ x = 0 or x – 5 = 0

⇒ x = 0 or 5

Quadratic Equations Exercise 5A: Ques No 5

x² – 3x – 10 = 0

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 Exercise 5A: Ques No 6

x² + x – 12 = 0

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

Quadratic Equations Exercise 5A: Ques No 7

2(x² + 1) = 5x

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

Maths Quadratic Equations Exercise 5A: Ques No 8

x(2x + 5) = 3

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

Class 10 Maths Quadratic Equations Exercise 5A: Ques No 9

4x² – 3x – 1 = 0

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

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

6x² – 13x + 5 = 0

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

Quadratic Equations Exercise 5A: Ques No 11

3x² – 5x – 12 = 0

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

Quadratic Equations Exercise 5A: Ques No 12

2x² – 11x + 5 = 0

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

Ques No 13

x/2 + 6/x = 4 

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.

Quadratic Equations Exercise 5A: Ques No 14

10x – 1/x = 3

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

ICSE Solutions Class 10 Exercise 5A: Ques No 15

9x + 1/x = 6

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

Ques No 16

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

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

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 Class 10 Maths Quadratic Equations Exercise 5A: Ques No 18

x/a – (a + b)/x = b(a + b)/ax

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)

Maths Quadratic Equations Exercise 5A: Ques No 19

1/(a + b + x) – 1/x = 1/a + 1/b

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

Class 10 Maths Quadratic Equations Exercise 5A: Ques No 20

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

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 – 8x² – 34x – 8 = 0

⇒ 9x² – 34x – 8 = 0

⇒ 9x² – 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

Class 10 Maths Quadratic Equations Exercise 5A: Ques No 21

2x/(x – 4) + (2x – 5)/(x – 3) = 25/3

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

Ques No 22

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

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

Ques No 23

√2x² – 3x – 2√2 = 0

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

Quadratic Equations Exercise 5A: Ques No 24

a(x² + 1) – x(a² + 1) = 0

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

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}

S Chand ICSE Class 10 Maths Chapterwise Notes & Solutions
Chapter 1 : GST Notes & Solutions | Notes | Exercise 1
Chapter 2 : Banking Notes & Solutions | Notes | Exercise 2 | Revision Exercise
Chapter 3 : Shares & Dividends Notes & Solutions | Notes | Exercise 3A | Exercise 3B | Revision Exercise
Chapter 4 : Linear Inequations in One Variable Notes & Solutions | Notes | Exercise 4 | Revision Exercise
Chapter 5 : Quadratic Equations Notes & Solutions | Notes | Exercise 5A | Exercise 5B | Exercise 5C| Exercise 5D| Exercise 5E| Revision Exercise
Chapter 6 : Ratios & Proportions Notes & Solutions | Notes | Exercise 6A | Exercise 6B | Exercise 6C| Revision Exercise

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