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Which answer best describes the complex zeros of the polynomial function?

f(x)=x^3+x^2−8x−8

A. The function has two real zeros and one nonreal zero. The graph of the function intersects the x-axis at exactly one location.

B. The function has three real zeros. The graph of the function intersects the x-axis at exactly three locations.

C. The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one location.

D. The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly two locations.

Guest Oct 2, 2018

CPhill · Answer 1 · 2018-10-02T04:13:15

x^3 + x^2 - 8x - 8 factor as

x^2 (x + 1) - 8 ( x + 1)

(x + 1) (x^2 - 8) =

(x + 1) (x + √8) (x - √8 )

Setting each factor to 0 and solving for x produces x = -1, x = -√8 , x = √8

So....three real roots ⇒ "B"