Which of the following is a zero of the polynomial x³ + 2x² - 5x - 6?

We need to do hit and trial to find root of a cubic equation.

If it is a root of equation, it must satisfy the equation.

So, let’s start with option A.

(-2)³ + 2(-2)² - 5(-2)-6 = -8 + 8 + 10 - 6 = 4

Let’s try option B

(2)³ + 2(2)² - 5(2)-6 = 8 + 8 – 10 - 6 = 0

Let’s try option C

(-3)³ + 2(-3)² - 5(-3)-6 = -27 + 18 + 15 - 6 = 0

For option D

(3)³ + 2(3)² - 5(3)-6 = 27 + 18 – 15 - 6 = 24

Hence Option B and C are correct

Verifying –

Factors of the given equation is (x-2)(x + 3)(x + 1) = x³ + 2x² - 5x - 6.