Find roots of polynomial $$ p(x) = x^6+2x^5+6x^4+8x^3+17x^2+18x+18 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.7071+1.5811i\\[1 em]x_2 &= 0.7071-1.5811i\\[1 em]x_3 &= -1+i\\[1 em]x_4 &= -1-i\\[1 em]x_5 &= -0.7071+1.5811i\\[1 em]x_6 &= -0.7071-1.5811i \end{aligned} $$Explanation
Polynomial $ x^6+2x^5+6x^4+8x^3+17x^2+18x+18 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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