Find roots of polynomial $$ p(x) = x^6+x^5-4x^4+x-1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.5381\\[1 em]x_2 &= -2.581\\[1 em]x_3 &= 0.5114+0.4064i\\[1 em]x_4 &= 0.5114-0.4064i\\[1 em]x_5 &= -0.49+0.5918i\\[1 em]x_6 &= -0.49-0.5918i \end{aligned} $$Explanation
Polynomial $ x^6+x^5-4x^4+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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