Question

Solve the following equation by factorisation method:

21x² + 8x − 4 = 0

Answer 1

Given:

21x² + 8x − 4 = 0

Find a × c

a = 21, b = 8, c = −4

a × c

= 21 × (−4)

= −84

Find two numbers whose product = −84 and sum = 8.

These numbers are:

14 and −6

21x² + 14x − 6x − 4 = 0

(21x² + 14x) + (−6x − 4) = 0

7x(3x + 2) −2(3x + 2) = 0

(3x + 2) (7x − 2) = 0

3x + 2 = 0

⇒ x = −`2/3`

7x − 2 = 0

⇒ x = `2/7` 

`x = -2/3 or x = 2/7`