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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 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.

 Oct 26, 2018
 #1
avatar+103049 
+2

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.

 

 

 

cool cool cool

 Oct 26, 2018
 #2
avatar+75 
+1

Gosh that's complicated : x

 Oct 26, 2018
 #3
avatar+103049 
0

HAHAHA!!!!!....not too hard,  MJ  !!!!!

 

cool cool cool

CPhill  Oct 26, 2018
 #4
avatar+75 
0

How does it work....? 

Sincerelyrose  Oct 26, 2018
 #5
avatar+103049 
0

Simple...

 

"Magic"   !!!!

 

[ As my Algebra 2 teacher used to say..... ] 

 

cool cool cool

CPhill  Oct 26, 2018

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