Find roots of polynomial $$ p(x) = 5x^6-4x^5+3x^4-2x^3+x^2-x+2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.5499+0.5439i\\[1 em]x_2 &= -0.5499-0.5439i\\[1 em]x_3 &= 0.1409+0.8974i\\[1 em]x_4 &= 0.1409-0.8974i\\[1 em]x_5 &= 0.8091+0.3945i\\[1 em]x_6 &= 0.8091-0.3945i \end{aligned} $$Explanation
Polynomial $ 5x^6-4x^5+3x^4-2x^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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