SOLUTION: Find a polynomial function of lowest degree with rationl coefficients that has the given numbers as some of its zeros. -8i, square root 8

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Question 141517: Find a polynomial function of lowest degree with rationl coefficients that has the given numbers as some of its zeros.
-8i, square root 8
Answer by solver91311(12126) About Me  (Show Source):
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Both complex and irrational roots come in conjugate pairs. That is, if you have a root of the form a%2Bbi, there must also be a root a-bi. Likewise, if a%2Bsqrt%28b%29 is a root, then a-sqrt%28b%29 is also a root.

Your roots are in these forms because -8i=0-8i and sqrt%288%29=0%2Bsqrt%288%29

A number alpha is a zero of a polynomial function if and only if x-alpha is a factor of the polynomial, so:

%28x-8i%29%28x%2B8i%29%28x-sqrt%288%29%29%28x%2Bsqrt%288%29%29 are the factors of your minimum (4th) degree polynomial. So get busy multiplying.