SOLUTION: Write a polynomial function with rational coefficients so that P(x)=0 has the given roots. 1.) -4 and 5i

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Question 745890: Write a polynomial function with rational coefficients so that P(x)=0 has the given roots.
1.) -4 and 5i
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
complex roots of polynomials with real always come in conjugate pairs so if 5i is a root, then so is -5i.
so the general polynomial is...

p=Q%28x%29%28x-4%29%28x-5i%29%28x%2B5i%29
but the principal polynomial is

p=%28x-4%29%28x-5i%29%28x%2B5i%29

%28x-4%29%28x%5E2%2B25%29

x%28x%5E2%2B25%29-4%28x%5E2%2B25%29

x%5E3%2B25x-4x%5E2-100%29

x%5E3-4x%5E2%2B25x-100%29