Find roots of polynomial $$ p(x) = 13x^{12}+9x^{10}+2x^8+12x^6+9 $$

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

$$ \begin{aligned}x_1 &= 0.7196+0.6826i\\[1 em]x_2 &= 0.7196-0.6826i\\[1 em]x_3 &= -0.7196+0.6826i\\[1 em]x_4 &= -0.7196-0.6826i\\[1 em]x_5 &= 0.8467+0.3258i\\[1 em]x_6 &= 0.8467-0.3258i\\[1 em]x_7 &= 0.097+1.0091i\\[1 em]x_8 &= 0.097-1.0091i\\[1 em]x_9 &= -0.8467+0.3258i\\[1 em]x_{10} &= -0.8467-0.3258i\\[1 em]x_{11} &= -0.097+1.0091i\\[1 em]x_{12} &= -0.097-1.0091i \end{aligned} $$

Polynomial $ 13x^{12}+9x^{10}+2x^8+12x^6+9 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.

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