Find roots of polynomial $$ p(x) = x^9-10x^8+40x^7-80x^6+80x^5-32x^4-1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 2.4831\\[1 em]x_2 &= 0.2257+0.4149i\\[1 em]x_3 &= 0.2257-0.4149i\\[1 em]x_4 &= -0.2793+0.2192i\\[1 em]x_5 &= -0.2793-0.2192i\\[1 em]x_6 &= 1.5752+0.515i\\[1 em]x_7 &= 1.5752-0.515i\\[1 em]x_8 &= 2.2368+0.4591i\\[1 em]x_9 &= 2.2368-0.4591i \end{aligned} $$Explanation
Polynomial $ x^9-10x^8+40x^7-80x^6+80x^5-32x^4-1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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