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

Solution:

The given function is

f(x) = x³ - 9x² + 20x

Let us take out x as common

f(x) = x(x² - 9x + 20)

Now by splitting the middle term

f(x) = x(x² -4x - 5x + 20)

So we get

f(x) = x [x(x - 4) - 5(x - 4)]

f(x) = x(x - 4)(x - 5)

Here

x = 0

x - 4 = 0 where x = 4

x - 5 = 0 where x = 5

Therefore, the zeros of the polynomial function is x = 0 or x = 4 or x = 5.

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

Summary:

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