Question

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.

Answer 1

The third choice: -4, 0, and 1

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