Asked by Dobi
Find the remaining zeros of the following polynomial given the P(i)=0.
x^4-8x^3+14x^2-8x+13
x^4-8x^3+14x^2-8x+13
Answers
Answered by
Steve
P(-i) is also zero, so (x^2+1) divided p(x).
(x^4-8x^3+14x^2-8x+13)/(x^2+1) = x^2-8x+13
So, all the roots of p(x)=0 are ±i and 4±√3
(x^4-8x^3+14x^2-8x+13)/(x^2+1) = x^2-8x+13
So, all the roots of p(x)=0 are ±i and 4±√3
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