Find roots of polynomial $$ p(x) = 11x^{10}+10x^9+18x^8+24x^7+7x^6+6x^5+40x^4+8x^3+3x^2-2x-8 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.5887\\[1 em]x_2 &= -0.687\\[1 em]x_3 &= -0.0869+0.6833i\\[1 em]x_4 &= -0.0869-0.6833i\\[1 em]x_5 &= 0.7667+0.7634i\\[1 em]x_6 &= 0.7667-0.7634i\\[1 em]x_7 &= 0.0263+1.4589i\\[1 em]x_8 &= 0.0263-1.4589i\\[1 em]x_9 &= -1.1115+0.5346i\\[1 em]x_{10} &= -1.1115-0.5346i \end{aligned} $$Explanation
Polynomial $ 11x^{10}+10x^9+18x^8+24x^7+7x^6+6x^5+40x^4+8x^3+3x^2-2x-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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