Question

Solve the following equation by factorization:

5x² – 12x – 9 = 0, when (i) x ∈ I (ii) x ∈ Q

Answer 1

Given,

⇒ 5x² – 12x – 9 = 0

⇒ 5x² – 15x + 3x – 9 = 0

⇒ 5x(x – 3) + 3(x – 3) = 0

⇒ (5x + 3)(x – 3) = 0

⇒ (5x + 3) = 0 or (x – 3) = 0   ...[Using zero-product rule]

⇒ 5x = –3 or x = 3

⇒ x = `(-3)/5` or x = 3

(i) Since, x ∈ I

Hence, x = {3}.

(ii) Since, x ∈ Q

Hence, `x = {3, (-3)/5}`.