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

Solution:

The given polynomial function is

f(x) = x³ - 10x² + 24x

Taking out x as common

f(x) = x(x² - 10x + 24)

Now splitting the middle term

f(x) = x [x² - 4x - 6x + 24]

f(x) = x[x (x - 4) - 6 (x - 4)]

f(x) = x(x - 4) (x - 6)

Here

x = 0, x - 4 = 0 and x - 6 = 0

x = 0, x = 4 and x = 6

Therefore, the zeros are 0, 4 and 6.

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.