SOLUTION: Please form a polynomial f(x) with real coefficients having the given degree and zeroes. Degree 4; Zeroes:-5-2i, -3; Multiplicity 2

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Question 921560: Please form a polynomial f(x) with real coefficients having the given degree and zeroes. Degree 4; Zeroes:-5-2i, -3; Multiplicity 2
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Multiplicity of 2 must be for the root -3. Complex roots with imaginary parts come as conjugate pair.

f%28x%29=%28x-%28-5-2i%29%29%28x-%28-5%2B2i%29%29%28x-%28-3%29%29%5E2
Work with that. Simplify in whatever form you need. Be sure to notice and take advantage of Difference of Square...

Skipping the showing of most of the steps, you should find these:
%28%28x%2B5%29%5E2%2B4%29%28x%2B3%29%5E2
highlight%28%28x%5E2%2B10x%2B29%29%28x%2B3%29%5E2%29, here kept still in the factored form.