SOLUTION: Thank you for your help solving. Solve x^4 - 2x^3 + 7x^2 - 10x + 10 = 0 given that 1 + i is a root.

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Question 889313: Thank you for your help solving.
Solve x^4 - 2x^3 + 7x^2 - 10x + 10 = 0 given that 1 + i is a root.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If 1%2Bi is a root, then 1-i is also a root since complex roots only occur in complex conjugate pairs.
%28x-%281%2Bi%29%29%28x-%281-i%29%29=x%5E2-%281-i%29x-%281%2Bix%29-%281%2Bi%29%281-i%29
%28x-%281%2Bi%29%29%28x-%281-i%29%29=x%5E2-2x%2B%281-i%2Bi-i%5E2%29%29
%28x-%281%2Bi%29%29%28x-%281-i%29%29=x%5E2-2x%2B%281%2B1%29%29
%28x-%281%2Bi%29%29%28x-%281-i%29%29=x%5E2-2x%2B2%29
Now use polynomial long division to factor out this polynomial.
.
Symbolically shown here, the divisor turns out to be,
x%5E2%2B5
So then,
x%5E4+-+2x%5E3+%2B+7x%5E2+-+10x+%2B+10=%28x%5E2-2x%2B2%29%28x%5E2%2B5%29
So the other two roots are also complex,
x=0+%2B-+5i