SOLUTION: Form a third-degree polynomial function with real coefficients such that 1+i and -5 are zeros?

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Question 914543: Form a third-degree polynomial function with real coefficients such that 1+i and -5 are zeros?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Bi =>complex root
and
-5 real root
Complex roots always come in complex conjugate pairs; so we have 1%2Bi and 1-i
f%28x%29=%28x-%281%2Bi%29%29%28x-%281-i%29%29%28x-%28-5%29%29

f%28x%29=+%28x-1-i%29%28x-1%2Bi%29+%28x%2B5%29 ....multiply



f%28x%29=%28x%5E2-2x%2B1-%28-1%29%29%28x%2B5%29

f%28x%29=%28x%5E2-2x%2B1%2B1%29%28x%2B5%29

f%28x%29=+%28x%5E2-2x%2B2%29%28x%2B5%29+

f%28x%29=x%5E3%2B5x%5E2+-2x%5E2-10x+%2B2x%2B10
f%28x%29=x%5E3%2B3x%5E2-8x%2B10

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+15%2C+x%5E3%2B3x%5E2-8x%2B10%29+