SOLUTION: Find a polynomial function of lowest degree with rational coefficients that has given numbers as some of its zeros. 2+i,4

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Question 374734: Find a polynomial function of lowest degree with rational coefficients that has given numbers as some of its zeros.
2+i,4
Answer by Fombitz(13828) About Me  (Show Source):
You can put this solution on YOUR website!
If x=2%2Bi is a zero so is x=2-i,
f%28x%29=%28x-4%29%28x-%282%2Bi%29%29%28x-%282-i%29%29
f%28x%29=%28x-4%29%28x%5E2-4x%2B5%29
highlight%28f%28x%29=x%5E3-8x%5E2%2B21x-20%29