Find roots of polynomial $$ p(x) = 23x^{17}+13x^4-46 $$

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

$$ \begin{aligned}x_1 &= 1.0195\\[1 em]x_2 &= 0.7857+0.7119i\\[1 em]x_3 &= 0.7857-0.7119i\\[1 em]x_4 &= -0.6302+0.8502i\\[1 em]x_5 &= -0.6302-0.8502i\\[1 em]x_6 &= -0.2641+0.9995i\\[1 em]x_7 &= -0.2641-0.9995i\\[1 em]x_8 &= 0.4506+0.9469i\\[1 em]x_9 &= 0.4506-0.9469i\\[1 em]x_{10} &= -0.9041+0.5424i\\[1 em]x_{11} &= -0.9041-0.5424i\\[1 em]x_{12} &= 0.0857+1.0178i\\[1 em]x_{13} &= 0.0857-1.0178i\\[1 em]x_{14} &= 0.9784+0.3571i\\[1 em]x_{15} &= 0.9784-0.3571i\\[1 em]x_{16} &= -1.0118+0.1735i\\[1 em]x_{17} &= -1.0118-0.1735i \end{aligned} $$

Polynomial $ 23x^{17}+13x^4-46 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.

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