SOLUTION: Find a polynomial equation with real coefficients that has the given roots. 44 and - 5i

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Question 1068173: Find a polynomial equation with real coefficients that has the given roots.
44 and - 5i
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Polynomials with real coefficients have complex roots in complex conjugate pairs.
f%28x%29=%28x-44%29%28x%2B5i%29%28x-5i%29
f%28x%29=%28x-44%29%28x%5E2%2B25%29
f%28x%29=x%5E3%2B25x-44x%5E2-1100
f%28x%29=x%5E3-44x%5E2%2B25x-1100

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
p(x) = (x-44)*(x-5i)*(x+5i) = (x-44)*(X+25).

For a polynomial with real coefficients, the complex roots goes in pairs:
a + bi and a - bi, the complex number and it conjugate.

Therefore, your polynomial has the complex roots 5i and -5i.