Find roots of polynomial $$ p(x) = 3x^9-7x^8-4x^6+5x^5-3x+8 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.0543\\[1 em]x_2 &= -0.9204\\[1 em]x_3 &= 2.4423\\[1 em]x_4 &= 0.6807+0.6663i\\[1 em]x_5 &= 0.6807-0.6663i\\[1 em]x_6 &= -0.687+0.8316i\\[1 em]x_7 &= -0.687-0.8316i\\[1 em]x_8 &= -0.1152+1.0259i\\[1 em]x_9 &= -0.1152-1.0259i \end{aligned} $$Explanation
Polynomial $ 3x^9-7x^8-4x^6+5x^5-3x+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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