Class 10 Maths

## NCERT Exercise 4.2

### Part 1

Question 1: Find the roots of the following quadratic equations by factorization:

(i) x^2 – 3x – 10 = 0

Solution: x^2 – 3x – 10 = 0

Or, x^2 – 5x + 2x – 10 = 0

Or, x(x – 5) + 2(x – 5) = 0

Or, (x + 2)(x – 5) = 0

Now; case 1: (x + 2) = 0

Or, x = - 2

Case 2: (x – 5) = 0

Or, x = 5

Hence, roots are: - 2 and 5

(ii) 2x^2 + x – 6

Solution: 2x^2 + x – 6 = 0

Or, 2x^2 + 4x – 3x – 6 = 0

Or, 2x(x + 2) – 3(x + 2) = 0

Or, (2x – 3)(x + 2) = 0

Case 1: (2x – 3) = 0

Or, 2x = 3

Or, x = 3/2

Case 2: (x + 2) = 0

Or, x = - 2

Hence, roots are – 2 and 3/2

(iii) sqrt2x^2 + 7x + 5sqrt2 = 0

Solution: sqrt2 x^2 + 7x + 5sqrt2 = 0

Or, sqrt2 x^2 + 2x + 5x + 5sqrt2 = 0

Or, sqrt2x(x + sqrt2) + 5(x + sqrt2) = 0

Or, (sqrt2x + 5)(x + sqrt2) = 0

Case 1: (sqrt2x + 5) = 0

Or, sqrt2x = 5

Or, x=-(5)/(sqrt2)

Case 2: (x + sqrt2) = 0

Or, x = - sqrt2

Hence, roots are;

-5/sqrt2 and -sqrt2

Question (iv): 2x^2-x+1/8=0

Solution:

2x^2-x+1/8=0

Or, (16x^2-8x+1)/(8)=0

Or, 16x^2-4x-4x+1=0

Or, 16x(x-1/4)-4(x-1/4)=0

Or, (16x-4)(x-1/4)

Hence, 16x-4=0

Or, 16x=4

Or, x=(4)/(16)=1/4

Similarly;

x-1/4=0

Or, x=1/4

Hence, ¼ is the root of this equation.

(v) 100x^2 – 20x + 1 = 0

Solution: 100x^2 – 20x + 1 = 0

Or, 100x^2 – 10x – 10x + 1 = 0

Or, 10x(10x – 1) – 1(10x – 1) = 0

Or, (10x – 1)(10x – 1) = 0

Hence; x = (1)/(10)