# 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 - 1 = 0

x = 1/4 and x = 1/4

Roots are: 1/4, 1/4

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

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

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

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

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

(10x - 1)^{2} = 0

10x - 1 = 0

x =1/10 and x = 1/10

Roots are: 1/10, 1/10

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 4

**Video Solution:**

## Find the roots of the following quadratic equations by factorization: (i) x² - 3x -10 = 0 (ii) 2x² + x - 6 = 0 (iii) √2x² + 7x + 5√2 = 0 (iv) 2x² - x + 1/ 8 = 0 (v) 100x² - 20x + 1= 0

Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.2 Question 1

**Summary:**

The roots of the quadratic equation by the method of the factorization for (i) x² - 3x -10 = 0 (ii) 2x² + x - 6 = 0 (iii) √2x² + 7x + 5√2 = 0 (iv) 2x² - x + 1/ 8 = 0 (v) 100x² - 20x + 1= 0 are (i) - 2, 5, (ii) 3/2, -2, (iii) - 5/√2, - √2, (iv) 1/4, 1/4 and (v) 1/10, 1/10 respectively.

**☛ Related Questions:**

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