# Find the roots of the following quadratic equations by factorisation:

(i) x^{2} - 3x -10 = 0

(ii) 2x^{2} + x - 6 = 0

(iii) √2x^{2} + 7x + 5√2 = 0

(iv) 2x^{2} - x + 1/ 8 = 0

(v) 100x^{2} - 20x + 1= 0

**Solution:**

The roots of the polynomial are the same as the zeros of the polynomial.

Therefore, roots can be found by factorizing the quadratic equation into two linear factors and after that equating each factor to zero.

(I) x^{2} - 3x -10 = 0

x^{2} - 5x + 2x -10 = 0

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

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

x - 5 = 0 and x + 2 = 0

x = 5 and x = - 2

Therefore, roots are : 2, 5.

(ii) 2x^{2} + x - 6 = 0

2x^{2} + 4x - 3x - 6 = 0

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

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

2x - 3 = 0 and x + 2 = 0

2x = 3 and x = - 2

x = 3/2 and x = - 2

Therefore, roots are: 3 / 2, -2

(iii) √2x^{2} + 7x + 5√2 = 0

√2x^{2} + 5x + 2x + 5√2 = 0

√2x^{2} + 2x + 5x + 5√2 = 0

(√2x + 5) (x + √2) = 0

√2x + 5 = 0 or x + √2 = 0

√2x = - 5 or x = - √2

x = (- 5)/√2 or x = - √2

Therefore, roots are: -5/√2, -√2

(iv) 2x^{2} - x + 1/ 8 = 0

Multiplying both sides of the equation by 8:

2(8) x^{2} - 8(x) + (8)(1/ 8) = (0)8

16x^{2} - 8x + 1 = 0

16x^{2} - 4x - 4x + 1 = 0

4x (4x - 1) -1 (4x - 1) = 0

(4x - 1) (4x - 1) = 0

(4x - 1)^{2} = 0

4x = 0

x = 1/4 and x = 1/4

Roots are: 1/4, 1/4

(v) 100x^{2} - 20x + 1 = 0

100x^{2} - 20 x + 1 = 0

100x^{2} - 10x - 10 x + 1 = 0

10x(10 x - 1) -1(10 x - 1) = 0

(10x - 1)(10 x - 1) = 0

10x - 1 = 0

10x = 1

x =1/10 and x = 1/10

Roots are: 1/10 , 1/10 .

**Video Solution:**

## Find the roots of the following quadratic equations by factorization: (i) x^{2} - 3x -10 = 0 (ii) 2x^{2} + x - 6 = 0 (iii) √2x^{2} + 7x + 5√2 = 0 (iv) 2x^{2} - x + 1/ 8 = 0 (v) 100x^{2} - 20x + 1= 0

### Class 10 Maths NCERT Solutions - Chapter 4 Exercise 4.2 Question 1:

Find the roots of the following quadratic equations by factorization:(i) x^{2} - 3x -10 = 0 (ii) 2x^{2} + x - 6 = 0 (iii) √2x^{2} + 7x + 5√2 = 0 (iv) 2x^{2} - x + 1/ 8 = 0 (v) 100x^{2} - 20x + 1= 0

Final Answer

The roots of the quadratic equation by the method of the factorization are (- 2, 5) for the first equation, (1/4, 1/4) for the second equation, and (1/10 , 1/10) for the third equation.