Find roots of polynomial $$ p(x) = 15x^9+6x^3-2x^2+9 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.8573\\[1 em]x_2 &= 0.4653+0.7651i\\[1 em]x_3 &= 0.4653-0.7651i\\[1 em]x_4 &= -0.7916+0.577i\\[1 em]x_5 &= -0.7916-0.577i\\[1 em]x_6 &= -0.134+0.984i\\[1 em]x_7 &= -0.134-0.984i\\[1 em]x_8 &= 0.8889+0.3635i\\[1 em]x_9 &= 0.8889-0.3635i \end{aligned} $$Explanation
Polynomial $ 15x^9+6x^3-2x^2+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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