Solve 2x^2 - 9x + 10 = 0 when x ∈ N x ∈ Q

2x 2 - 9x + 10 = 0 ⇒ 2x 2 - 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 = or x = 2. (i) Since, x ∈ N Hence, value of x = 2. (ii) Since, x ∈ Q Hence, value of x = or 2.