SOLUTION: Really need some help. Use the given zero to find the remaining zeros of the function. f(x)=x^3-9x^2+9x-81 zero: 3 i
Enter the remaining zeros of f.
Any help would be appr
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Question 767477: Really need some help. Use the given zero to find the remaining zeros of the function. f(x)=x^3-9x^2+9x-81 zero: 3 i
Enter the remaining zeros of f.
Any help would be appreciated.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If 
is a zero of a polynomial function, then the conjugate, 
must also be a zero. That is because complex roots always come in conjugate pairs.
So if 
is a zero, 
must also be a zero. That means that both 
and 
must both be factors of the polynomial. The product of a pair of conjugates is the difference of two squares so:
(x\ +\ 3i)\ =\ x^2\ -\ (-9)\ =\ x^2\ +\ 9)
Divide the original polynomial by 
using polynomial long division. The quotient will be the remaining factor from which solving for the remaining zero is trivial.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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