Find roots of polynomial $$ p(x) = x^6-306x^5-1123x^4-1633x^3-1123x^2-306x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.0032\\[1 em]x_2 &= 309.6438\\[1 em]x_3 &= -0.8282+0.5604i\\[1 em]x_4 &= -0.8282-0.5604i\\[1 em]x_5 &= -0.9953+0.0965i\\[1 em]x_6 &= -0.9953-0.0965i \end{aligned} $$Explanation
Polynomial $ x^6-306x^5-1123x^4-1633x^3-1123x^2-306x+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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