Find roots of polynomial $$ p(x) = 3x^{12}-22x-8 $$

The roots of polynomial $ p(x) $ are:

$$ \begin{aligned}x_1 &= -0.3636\\[1 em]x_2 &= 1.2272\\[1 em]x_3 &= -1.1103+0.3404i\\[1 em]x_4 &= -1.1103-0.3404i\\[1 em]x_5 &= -0.7489+0.9114i\\[1 em]x_6 &= -0.7489-0.9114i\\[1 em]x_7 &= 0.5282+1.0942i\\[1 em]x_8 &= 0.5282-1.0942i\\[1 em]x_9 &= -0.138+1.1918i\\[1 em]x_{10} &= -0.138-1.1918i\\[1 em]x_{11} &= 1.0373+0.6501i\\[1 em]x_{12} &= 1.0373-0.6501i \end{aligned} $$

Polynomial $ 3x^{12}-22x-8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.

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