Question

Solve the following equation by factorization:

2x² – 11x + 15 = 0, when (i) x ∈ N (ii) x ∈ I

Answer 1

Given,

⇒ 2x² – 11x + 15 = 0

⇒ 2x² – 6x – 5x + 15 = 0

⇒ 2x(x – 3) – 5(x – 3) = 0

⇒ (2x – 5)(x – 3) = 0

⇒ (2x – 5) = 0 or (x – 3) = 0   ...[Using zero-product rule]

⇒ 2x = 5 or x = 3

⇒ x = `5/2` or x = 3

(i) Since, x ∈ N

Hence, x = {3}.

(ii) Since, x ∈ I

Hence, x = {3}.