Question

Solve the following equation by factorization:

2x² – 9x + 10 = 0, when (i) x ∈ N (ii) x ∈ Q

Answer 1

Given,

⇒ 2x² – 9x + 10 = 0

⇒ 2x² – 4x – 5x + 10 = 0

⇒ 2x(x – 2) – 5(x – 2) = 0

⇒ (2x – 5)(x – 2) = 0

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

⇒ 2x = 5 or x = 2

⇒ x = `5/2` or x = 2

(i) Since, x ∈ N

Hence, value of x = {2}.

(ii) Since, x ∈ Q

Hence, `x = {2, 5/2}`.