Find roots of polynomial $$ p(x) = x^6+x^5+x^4+9x^3-x^2+5x-8 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.762\\[1 em]x_2 &= -2.4262\\[1 em]x_3 &= -0.361+1.0008i\\[1 em]x_4 &= -0.361-1.0008i\\[1 em]x_5 &= 0.6931+1.8283i\\[1 em]x_6 &= 0.6931-1.8283i \end{aligned} $$Explanation
Polynomial $ x^6+x^5+x^4+9x^3-x^2+5x-8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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