SOLUTION: form a polynomial with a degree:5 zeros: -5;-i,-9+i
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Question 974906: form a polynomial with a degree:5 zeros: -5;-i,-9+i
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Complex zeros of polynomials always occur in conjugate pairs. Hence if 
is a zero of a polynomial then 
is a zero as well.
Your five zeros are 
, 
, 
, 
, and 
.
If 
is a zero of a polynomial in 
, then 
is a factor of the polynomial.
Your five factors are therefore:
(x\ +\ i)(x\ -\ i)(x\ +\ 9\ -\ i)(x\ +\ 9\ +\ i))
Just multiply the five factors together and collect like terms. I'll get you started by multiplying the complex factors to get rid of all the imaginary parts.
(x^2\ +\ 1)(x^2\ +\ 18x\ +\ 82))
You can do the rest yourself.
John
My calculator said it, I believe it, that settles it
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