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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
 #1
avatar+92506 
+1

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"

 

 

cool cool cool

CPhill  Oct 2, 2018

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