What are the zeros of the function what are their multiplicities f(x) = 5x³ - 5x² - 30x

Solution:

Given the function, f(x) = 5x³ - 5x² - 30x

To find zeros f(x) =0

5x³ - 5x² - 30x = 0

5x(x² - x - 6) = 0

5x = 0 ⇒ x = 0

(x² - x - 6) = 0

x² - 3x + 2x - 6 = 0

x(x - 3) + 2(x - 3) = 0

(x + 2)(x - 3) = 0

x + 2 = 0 ⇒ x = -2

x - 3 = 0 ⇒ x = 3

Therefore, the zeros are -2, 0, 3.

What are the zeros of the function what are their multiplicities f(x) = 5x³ - 5x² - 30x

Summary:

The zeros of the function f(x) = 5x³ - 5x² - 30x are -2, 0, 3.