SOLUTION: find a 4th degree polynomial with real coefficients satisfying the given conditions: -1,5, and 2+4i are zeros; f(1)=-272

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Question 1169061: find a 4th degree polynomial with real coefficients satisfying the given conditions: -1,5, and 2+4i are zeros; f(1)=-272
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


Complex zeros always appear in conjugate pairs, so if is a zero, then must also be a zero.

Your desired function then has 5 factors, one of which is a constant, thus:



You can expand and collect like terms for yourself. Hint: Remember that the product of two conjugates is the difference of two squares and that .

Substitute 1 for , then do the arithmetic to solve for giving you everything you need for your function.

John

My calculator said it, I believe it, that settles it

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I > Ø