Find roots of polynomial $$ p(x) = 6x^6+x^5-5x^4+2x^3+x^2+x+6 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.947+0.5186i\\[1 em]x_2 &= 0.947-0.5186i\\[1 em]x_3 &= -0.0018+0.8632i\\[1 em]x_4 &= -0.0018-0.8632i\\[1 em]x_5 &= -1.0286+0.3058i\\[1 em]x_6 &= -1.0286-0.3058i \end{aligned} $$Explanation
Polynomial $ 6x^6+x^5-5x^4+2x^3+x^2+x+6 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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