SOLUTION: Find a polynomial equation with real coefficients that has the given roots 5 and -3i x^3- ___x^2+_____x=0

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Question 1128379: Find a polynomial equation with real coefficients that has the given roots
5 and -3i
x^3- ___x^2+_____x=0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find a polynomial equation with real coefficients that has the given roots

x%5B1%5D=5 and x%5B2%5D=-3i+-> complex roots coming in pairs, so we also have x%5B3%5D=3i+
%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
%28x%29=%28x-5%29%28x-%28-3i%29%29%28x-3i%29
f%28x%29=%28x-5%29%28x%2B3i%29%28x-3i%29
f%28x%29=%28x-5%29%28x%5E2-%283i%29%5E2%29
f%28x%29=%28x-5%29%28x%5E2-9i%5E2%29
f%28x%29=%28x-5%29%28x%5E2-9%28-1%29%29
f%28x%29=%28x-5%29%28x%5E2%2B9%29
f%28x%29=x%5E3-5x%5E2%2B9x-45

x%5E3-+5x%5E2%2B9x-45=0