SOLUTION: Find a third degree polynomial equation with rational coeffients that has roots -2 and 5+i

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Question 1009592: Find a third degree polynomial equation with rational coeffients that has roots -2 and 5+i
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

given roots: x%5B1%5D=+-2 and x%5B2%5D=5%2Bi
since complex root always coming in pairs, we also have x%5B3%5D=5-i
use zero product theorem:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=%28x-%28-2%29%29%28x-%285%2Bi%29%29%28x-%285-i%29%29
f%28x%29=%28x%2B2%29%28x-5-i%29%28x-5%2Bi%29
f%28x%29=%28x%2B2%29%28x%5E2-5x%2Bxi-5x-5%28-5%29-5i-xi-i%28-5%29-i%2Ai%29
f%28x%29=%28x%2B2%29%28x%5E2-5x%2Bxi-5x%2B25-5i-xi%2B5i-i%5E2%29

f%28x%29=%28x%2B2%29%28x%5E2-10x%2B25%2B1%29
f%28x%29=%28x%2B2%29%28x%5E2-10x%2B26%29
f%28x%29=x%5E3-10x%5E2%2B26x%2B2x%5E2-20x%2B52
f%28x%29=x%5E3-8x%5E2%2B6x%2B52