What are the zeros of the function?

f (x) = 2x^3+6x^2-8x

-1,2, and 4.

-1,0, and 4.

-4,0, and 1.

-4,1, and 2.

The third choice: - 4, 0, and 1

Step-by-step explanation:

Finding zeroes is another way of saying solve ... set the equation equal to zero and solve ...

0 = 2x³ + 6x² - 8x

0 = 2x (x² + 3x - 4) (factor out a 2x from all three terms)

0 = 2x (x + 4) (x - 1) (factor x² + 3x - 4)

So

2x = 0 then x = 0

x + 4 = 0 then x = - 4

x - 1 = 0 then x = 1

Our zeroes are - 4, 0, and 1