Find roots of polynomial $$ p(x) = x^6+x^5+x^4+x^3+x^2+x-27 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.4533\\[1 em]x_2 &= -1.8678\\[1 em]x_3 &= 0.7102+1.5658i\\[1 em]x_4 &= 0.7102-1.5658i\\[1 em]x_5 &= -1.003+1.5359i\\[1 em]x_6 &= -1.003-1.5359i \end{aligned} $$Explanation
Polynomial $ x^6+x^5+x^4+x^3+x^2+x-27 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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