SOLUTION: degree 4, zeros -5+2i,-2 multiplicity 2

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Question 1187870: degree 4, zeros -5+2i,-2 multiplicity 2
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

Each zero 'a' gives a factor 'x-a', and noting complex zeros come in
conjugate pairs:
(x-(-5+2i))(x-(-5-2i))*(x+2)(x+2)
... after combining the terms with complex roots, and multiplying (x+2)(x+2) ...
= %28x%5E2%2B10x%2B29%29 * %28x%5E2%2B4x%2B4%29
... after expansion and subsquent simplification ...
= +x%5E4%2B14x%5E3%2B73x%5E2%2B156x%2B116+
( checked on WolframAlpha: ' factor x^4+14x^3+73x^2+156x+116 ' yields
+%28x%2B2%29%5E2+%28x%2B%285-2i%29%29%28x%2B%285%2B2i%29%29+ )