Solve the following equation by factorization:

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

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 = $\dfrac{5}{2}$ or x = 3.

(i) Since, x ∈ N

Hence, x = {3}.

(ii) Since, x ∈ I

Hence, x = {3}.