SOLUTION: find an nth degree polynomial function with real coefficients satisfying the given conditions n=3 f(-1)=20 3 and 2i are zeros

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Question 1098425: find an nth degree polynomial function with real coefficients satisfying the given conditions n=3 f(-1)=20 3 and 2i are zeros
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

If the coefficients are real and one root is 2i, then another root is -2i.

Since the polynomial is degree 3, we know all the roots.

The polynomial factors corresponding to the roots 3, 2i, and -2i are %28x-3%29 and x%5E2%2B4.

The polynomial is then
a%28x-3%29%28x%5E2%2B4%29

The constant a is determined by knowing that f(-1)=20:

a%28-1-3%29%281%2B4%29+=+20
a%28-4%29%285%29+=+20
-20a+=+20
a+=+-1

The polynomial is

-1%28x-3%29%28x%5E2%2B4%29
or
-x%5E3%2B3x%5E2-4x%2B12