What are the zeros of the polynomial function f(x) = x³ - x² - 12x?

Solution:

Given function is f(x) = x³ - x² - 12x

To find zeros of the polynomial we have to take f(x) = 0

f(x) = x³ - x² - 12x = 0

x(x² - x -12) = 0

x(x² - 4x + 3x -12) = 0

x[x(x - 4) + 3(x - 4)] = 0

x(x - 4)(x + 3) = 0

The roots are ⇒ x = 0,

x - 4 = 0 ⇒ x = 4

x + 3 = 0 ⇒ x = -3

What are the zeros of the polynomial function f(x) = x³ - x² - 12x?

Summary:

The zeros of the polynomial function f(x) = x³ - x² - 12x are 0, 4 and -3.