What are the zeros of polynomial function f(x) = x³ + 9x² + 20x?

Solution:

Given, the function is f(x) = x³ + 9x² + 20x.

We have to find the zeros of the polynomial function.

Taking out x as common,

f(x) = x³ + 9x² + 20x

f(x) = x(x² + 9x + 20)

Factoring x² + 9x + 20

= x² + 4x + 5x + 20

= x(x + 4) + 5(x + 4)

= (x + 5)(x + 4)

So, f(x) = x(x + 5)(x + 4)

Let f(x) = 0

x(x + 5)(x + 4) = 0

x = 0

x + 5 = 0 ⇒ x = -5

x + 4 = 0 ⇒ x = -4

Therefore, the zeros of the polynomial function are x = 0, -4 and -5.

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What are the zeros of polynomial function f(x) = x³ + 9x² + 20x?

Summary:

The zeros of the polynomial function f(x) = x³ + 9x² + 20x are x = 0, -4 and -5.