Find roots of polynomial $$ p(x) = x^6+129x^5+6831x^4+189783x^3+2913084x^2+x+76527504 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.8097+4.9366i\\[1 em]x_2 &= 0.8097-4.9366i\\[1 em]x_3 &= -16.0422+29.3027i\\[1 em]x_4 &= -16.0422-29.3027i\\[1 em]x_5 &= -49.2675+17.6855i\\[1 em]x_6 &= -49.2675-17.6855i \end{aligned} $$Explanation
Polynomial $ x^6+129x^5+6831x^4+189783x^3+2913084x^2+x+76527504 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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