+309 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 one location.
B) The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly two locations.
C) The function has three real zeros. The graph of the function intersects the x-axis at exactly three locations.
D) The function has two real zeros and one nonreal zero. The graph of the function intersects the x-axis at exactly one location.
+129852 x^3 + x^2 - 8x - 8 = 0
Factor as
x^2 ( x + 1) - 8 (x + 1) = 0
(x + 1) ( x^2 - 8) = 0
So either or
x + 1 = 0 x^2 - 8 = 0
And x = -1 ( x - √8) ( x + √8) = 0
x - √8 = 0 or x + √8 = 0
And x = √8 x = - √8
So
C) The function has three real zeros. The graph of the function intersects the x-axis at exactly three locations.
