SOLUTION: Write a polynomial function of degree 5 with zeros -1,2 and i. Justify your answer.

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Question 1080085: Write a polynomial function of degree 5 with zeros -1,2 and i. Justify your answer.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you mean with real coefficients so the complex roots are in complex conjugate pairs.
However, that polynomial would only need 4 zeros to specify it so the fifth zero is arbitrary.
I will make it 4th degree and you can check your problem setup and repost if necessary.
f%28x%29=%28x%2B1%29%28x-2%29%28x%2Bi%29%28x-i%29
f%28x%29=%28x%5E2-x-2%29%28x%5E2%2B1%29
f%28x%29=%28x%5E4-x%5E3-2x%5E2%29%2B%28x%5E2-x-2%29
f%28x%29=x%5E4-x%5E3-x%5E2-x-2
So for example, I can add x=0 as a root,
f%28x%29=x%28x%5E4-x%5E3-x%5E2-x-2%29
f%28x%29=x%5E5-x%5E4-x%5E3-x%5E2-2x