Find roots of polynomial $$ p(x) = x^6-x^5+3x^4+3x^3+3x^2+2x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.0171+0.7532i\\[1 em]x_2 &= 0.0171-0.7532i\\[1 em]x_3 &= -0.538+0.3642i\\[1 em]x_4 &= -0.538-0.3642i\\[1 em]x_5 &= 1.021+1.7698i\\[1 em]x_6 &= 1.021-1.7698i \end{aligned} $$Explanation
Polynomial $ x^6-x^5+3x^4+3x^3+3x^2+2x+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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