Question

Solve the following equation by factorisation method:

8x² − 22x − 21 = 0

Answer 1

Given:

8x² − 22x − 21 = 0

Find a × c

a = 8, b = −22, c = −21

a × c

= 8 × (−21)

= −168

Find two numbers whose product = −168 and sum = −22.

These numbers are:

−28 and +6

Rewrite and factorise

8x² − 28x + 6x − 21 = 0

(8x² − 28x) + (6x − 21) = 0

4x (2x − 7) + 3(2x − 7) = 0

(2x − 7) (4x + 3) = 0

2x − 7 = 0

⇒ x = `7/2`

4x + 3 = 0

⇒ x = −`3/4`

`x = 7/2 or x = -3/4`