SOLUTION: Finding polynomial having degree and zeros: Degree: 5 Zeros: 7, -i, -6+i

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Question 962604: Finding polynomial having degree and zeros:
Degree: 5 Zeros: 7, -i, -6+i

Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Finding polynomial having degree and zeros:
Degree: 5 Zeros: 7, -i, -6+i
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Complex solutions are in conjugate pairs, so the zeroes are:
6, -i, +i, -6+i, -6-i
--> (x-6)*(x-i)*(x+i)*(x+6+i)*(x+6-i)
You can do the multiplication.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Zeros: 7, -i, -6%2Bi
if -i is zero, then i is zero too
if -6%2Bi is zero, then -6-i is zero too
so, your polynomial is:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29%28x-x%5B5%5D%29
f%28x%29=%28x-7%29%28x-i%29%28x%2Bi%29%28x-%28-6%2Bi%29%29%28x-%28-6-i%29%29
f%28x%29=%28x-7%29%28x%5E2-i%5E2%29%28x%2B6-i%29%28x%2B6%2Bi%29
f%28x%29=%28x-7%29%28x%5E2-i%5E2%29%28x%5E2%2B6x%2Bx%2Ai%2B6x%2B36%2B6i-x%2Ai-6i-i%5E2%29
f%28x%29=%28x-7%29%28x%5E2%2B1%29%28x%5E2%2B12x%2B37%29
f%28x%29=%28x%5E3-7x%5E2%2Bx-7%29%28x%5E2%2B12x%2B37%29
f%28x%29=%28x%5E3-7x%5E2%2Bx-7%29%28x%5E2%2B12x%2B37%29
f%28x%29=x%5E5%2B5x%5E4-46x%5E3-254x%5E2-47x-259