SOLUTION: Find a cubic polynomial in standard form with real coefficients having the given zeros 1 & 1+2i

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Question 1078910: Find a cubic polynomial in standard form with real coefficients having the given zeros 1 & 1+2i
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
1 & 1%2B2i
if we have 1%2B2i, than we have also 1-2i, complex solutions come always in pairs
so, we use zero product formula to find equation:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29....plug in x%5B1%5D=1, x%5B2%5D=1%2B2i, and x%5B3%5D=1-2i

f%28x%29=%28x-1%29%28x-%281%2B2i%29%29%28x-%281-2i%29%29
f%28x%29=%28x-1%29%28x-1-2i%29%28x-1%2B2i%29
f%28x%29=%28x%5E2-2x+%2B+2i%281-x%29+%2B+1%29%28x-1%2B2i%29
f%28x%29=%28x%5E2-2x+%2B+2i%281-x%29+%2B+1%29%28x-1%2B2i%29
f%28x%29=x%5E3+-+3x%5E2+%2B+7x+-+5

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3+-+3x%5E2+%2B+7x+-+5%29+