Find roots of polynomial $$ p(x) = x^6-x^5-6x^4-x^2+x+10 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.22\\[1 em]x_2 &= -1.9382\\[1 em]x_3 &= 1.1393\\[1 em]x_4 &= 2.9898\\[1 em]x_5 &= 0.0145+1.1142i\\[1 em]x_6 &= 0.0145-1.1142i \end{aligned} $$Explanation
Polynomial $ x^6-x^5-6x^4-x^2+x+10 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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