Question

Of the following quadratic equations, which is the one whose roots are 2 and – 15 ?

(a) x² - 2x + 15 = 0

(b) x² + 15x - 2 = 0

(c) x² + 13x - 30 = 0

(d) x² - 30 = 0

Answer 1

(c) x² + 13x - 30 = 0

• x² - 2x + 15 = 0

⇒ (x - 5)(x + 2) = 0 ⇒ x = 5, -2

• x² + 15x - 2 = 0. Solving x ≠ 2, -15

• x² + 13x - 30 = 0

⇒ (x + 15)(x - 2) = 0 ⇒ x = -15, 2

• x² - 30 = 0 ⇒ x² = 30 ⇒ x = ±\(\sqrt{30}.\)