Question

Mark (✓) against the correct answer in each of the following:
Which of the following are zeros of the polynomial x³ + 2x² − 5x − 6?
(a) −2
(b) 2
(c) −3
(d) 3

Answer 1

(b) 2 and (c) −3
Let f(x) = x³ + 2x² − 5x − 6.
We have to find the zeros of the polynomial.
⇒ f(x) = 0
⇒ x³ + 2x² − 5x − 6 = 0
⇒ x³ + 3x² −x² −3x −2x −6 = 0
⇒ x²(x + 3) −x(x + 3) −2(x + 3) = 0
⇒ (x + 3)(x² − x − 2)
⇒ (x + 3)(x² − 2x + x − 2)
⇒ (x + 3){x(x − 2) +1(x − 2)} = 0
⇒ (x + 3)(x − 2)(x + 1) = 0
Either x + 3 = 0 or x − 2 = 0 or x + 1 = 0
⇒ x = − 3 or 2 or −1

Disclaimer: Here both 2 and − 3 are correct answers.