What Are the Zeros of the Polynomial Function f(x) = x³ – 9x² – 20x?

To find the zeros of the polynomial function f(x) = x³ – 9x² – 20x, we need to set the function equal to zero:

f(x) = x³ – 9x² – 20x = 0

First, we can factor out the common term, which in this case is x:

x(x² – 9x – 20) = 0

This gives us one zero, which is x = 0.

Next, we need to solve the quadratic equation x² – 9x – 20 = 0. We can factor this quadratic as well:

(x – 10)(x + 2) = 0

Setting each factor equal to zero gives us the other two zeros:

1. x – 10 = 0 → x = 10
2. x + 2 = 0 → x = -2

In summary, the zeros of the polynomial function f(x) = x³ – 9x² – 20x are:

• x = 0
• x = 10
• x = -2