SOLUTION: Q has degree 3 and zeros -5 and 1+i. find a polynomial that satisfies the given conditions.

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Question 835397: Q has degree 3 and zeros -5 and 1+i. find a polynomial that satisfies the given conditions.
Answer by reviewermath(1029) About Me  (Show Source):
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Question:
Q has degree 3 and zeros -5 and 1+i. find a polynomial that satisfies the given conditions.
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Answer:
If 1 + i is a root of Q, then its conjugate, 1 - i is also a root.
Sum of imaginary roots: (1 + i) + (1 - i) = 2
Product of imaginary roots: (1 + i)(1 - i) = 2
Quadratic Equation: x%5E2+-+%28sum%29x+%2B+product+=+0
x%5E2+-+2x+%2B+2+=+0
Cubic Equation: %28x%5E2+-+2x+%2B+2%29%28x+%2B+5%29+=+0 or
x%5E3+%2B+3x%5E2+-+8x+%2B+10+=+0
The polynomial function is highlight%28Q%28x%29+=+x%5E3+%2B+3x%5E2+-+8x+%2B+10%29