Find all of the real and imaginary zeros for the polynomial function

Mar 2010
27
0
[Solved]Find all of the real and imaginary zeros for the polynomial function

Find all of the real and imaginary zeros for the polynomial function f(x)=x^3-7x^2+x-7 Answer is 7,-i,i How do I solve this to get to the answer
 
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Jhevon

MHF Hall of Honor
Feb 2007
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New York, USA
Find all of the real and imaginary zeros for the polynomial function f(x)=x^3-7x^2+x-7 Answer is 7,-i,i How do I solve this to get to the answer
Factor by grouping

\(\displaystyle x^3 - 7x^2 + x - 7 = x^2(x - 7) + (x - 7)\)

\(\displaystyle = (x - 7)(x^2 + 1)\)

Now do you see how to get to the answer?
 

Plato

MHF Helper
Aug 2006
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\(\displaystyle x^3-7x^2+x-7=x^2(x-7)+(x-7)=(x-7)(x^2+1)\)
 
Mar 2010
27
0
Factor by grouping

\(\displaystyle x^3 - 7x^2 + x - 7 = x^2(x - 7) + (x - 7)\)

\(\displaystyle = (x - 7)(x^2 + 1)\)

Now do you see how to get to the answer?
so if i set this equal to zero i get the answer