SOLUTION: Find all the roots, given that x=2+i is a root: p(x)=x^4-4x^3+3x^2+8x-10

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Question 1113728: Find all the roots, given that x=2+i is a root:
p(x)=x^4-4x^3+3x^2+8x-10
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Another root is highlight%282-i%29, so part of the factorization for p is %28x-%282%2Bi%29%29%28x-%282-i%29%29
%28x-2-i%29%28x-2%2Bi%29
%28%28x-2%29-i%29%28%28x-2%29%2Bi%29
%28x-2%29%5E2%2B1
x%5E2-4x%2B4%2B1
x%5E2-4x%2B5--------a quadratic factor of p.

If you perform polynomial division for p(x) divided by x%5E2-4x%2B5, the result will be quotient of x%5E2-2. The roots corresponding to this are highlight%28-sqrt%282%29%29 and highlight%28sqrt%282%29%29.