What are the zeros of the polynomial function f(x) = x³ + 10x² + 24x?

Solution:

Given polynomial function f(x) = x³ + 10x² + 24x

f(x) = x³ + 10x² + 24x = 0

x(x² + 10x + 24) = 0

x(x² + 6x + 4x + 24) = 0

x [x(x + 6) + 4(x + 6)] = 0

x(x + 6)(x + 4) = 0

⇒ x = 0

⇒ (x + 6) = 0

x = -6

⇒ (x + 4) = 0

x = -4

What are the zeros of the polynomial function f(x) = x³ + 10x² + 24x?

Summary:

The zeros of the polynomial function f(x) = x³ + 10x² + 24x are 0,-4 and -6.