Find roots of polynomial $$ p(x) = 2x^6+2x^5+8x^4+2x^3+x^2+x+6 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.6128+0.6441i\\[1 em]x_2 &= 0.6128-0.6441i\\[1 em]x_3 &= -0.7505+0.6464i\\[1 em]x_4 &= -0.7505-0.6464i\\[1 em]x_5 &= -0.3623+1.9332i\\[1 em]x_6 &= -0.3623-1.9332i \end{aligned} $$Explanation
Polynomial $ 2x^6+2x^5+8x^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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