SOLUTION: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree:4; zeros: -5-3i; -4 multiplicity 2

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Question 1152238: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree:4; zeros: -5-3i; -4 multiplicity 2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Degree 4;
zeros:
x%5B1%5D=-5-3i, -> complex zeros always com in pairs, so you also have
x%5B2%5D=-5%2B3i
x%5B3%5D=-4 ->multiplicity 2, so you have one more same zero
x%5B4%5D=-4
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29
f%28x%29=%28x-%28-5-3i%29%29%28x-%28-5%2B3i%29%29%28x-%28-4%29%29%28x-%28-4%29%29
f%28x%29=%28x%2B5%2B3i%29%28x%2B5-3i%29%28x%2B4%29%28x%2B4%29
f%28x%29=%28x%5E2%2B10x%2B34%29%28x%2B4%29%5E2
f%28x%29=%28x%5E2%2B10x%2B34%29%28x%5E2%2B8x%2B16%29
f%28x%29=x%5E4%2B+18x%5E3%2B+130x%5E2%2B+432x%2B+544+++