Find roots of polynomial $$ p(x) = x^6+3x^5+5x^4+5x^3+5x^2+2x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.191+0.5878i\\[1 em]x_2 &= -0.191-0.5878i\\[1 em]x_3 &= i\\[1 em]x_4 &= -i\\[1 em]x_5 &= -1.309+0.9511i\\[1 em]x_6 &= -1.309-0.9511i \end{aligned} $$Explanation
Polynomial $ x^6+3x^5+5x^4+5x^3+5x^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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