Find roots of polynomial $$ p(x) = x^6-x^5+x^4-x^3+x^2-x+2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.177+1.1227i\\[1 em]x_2 &= 0.177-1.1227i\\[1 em]x_3 &= -0.7227+0.7741i\\[1 em]x_4 &= -0.7227-0.7741i\\[1 em]x_5 &= 1.0456+0.536i\\[1 em]x_6 &= 1.0456-0.536i \end{aligned} $$Explanation
Polynomial $ x^6-x^5+x^4-x^3+x^2-x+2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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