Question

PLZ HELP FOR BRAINLIEST!!



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

f(x)=x^3+x^2−8x−8


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


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


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


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

Answer 1

C

Using Descartes' rule of signs

look for the number of sign changes in f(x)

+ / + / - / -

There is 1 sign change hence 1 positive zero

f(-x) = -x³ + x² + 8x - 8

look for the number of sign changes in f(- x)

- / + / + / -

there are 2 sign changes hence 2 possible negative zeros