Find roots of polynomial $$ p(x) = x^6+x^5+x^4+x^3+x^2+x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.6235+0.7818i\\[1 em]x_2 &= 0.6235-0.7818i\\[1 em]x_3 &= -0.2225+0.9749i\\[1 em]x_4 &= -0.2225-0.9749i\\[1 em]x_5 &= -0.901+0.4339i\\[1 em]x_6 &= -0.901-0.4339i \end{aligned} $$Explanation
Polynomial $ x^6+x^5+x^4+x^3+x^2+x+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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