Solve the following equation by factorization:

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

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 = $\dfrac{5}{2}$ or x = 2.

(i) Since, x ∈ N

Hence, value of x = {2}.

(ii) Since, x ∈ Q

Hence, x = $\Big{2, \dfrac{5}{2}\Big}$.