Question

Solve the following equation by factorization:

4x² – 9x – 100 = 0, when x ∈ Q

Answer 1

Given,

⇒ 4x² – 9x – 100 = 0

⇒ 4x² + 16x – 25x – 100 = 0

⇒ 4x(x + 4) – 25(x + 4) = 0

⇒ (4x – 25)(x + 4) = 0

⇒ 4x – 25 = 0 or x + 4 = 0   ...[Using zero-product rule]

⇒ 4x = 25 or x = –4

⇒ x = `25/4` or x = –4

Since, x ∈ Q

Hence, `x = {-4, 25/4}`.