SOLUTION: Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 4-i, square root 6

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Question 869101: Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros.
4-i, square root 6
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Complex roots always come in complex conjugate pairs.
Since 4-i is a root, then so is 4%2Bi}.
In order to have rational coefficients, you ned to have a difference of squares to eliminate the sqrt%286%29.
f%28x%29=%28x-sqrt%286%29%29%28x%2Bsqrt%286%29%29%28x-%284-i%29%29%28x-%284%2Bi%29%29
f%28x%29=%28x%5E2-6%29%28x%5E2-8x%2B17%29
f%28x%29=x%5E4-8x%5E3%2B11x%5E2%2B48x-102