Find roots of polynomial $$ p(x) = x^9-5x^8+10x^7+5x^5-x^4-1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.6814\\[1 em]x_2 &= 0.3411+0.6044i\\[1 em]x_3 &= 0.3411-0.6044i\\[1 em]x_4 &= -0.5521+0.3254i\\[1 em]x_5 &= -0.5521-0.3254i\\[1 em]x_6 &= -0.2369+0.7984i\\[1 em]x_7 &= -0.2369-0.7984i\\[1 em]x_8 &= 2.6073+1.9745i\\[1 em]x_9 &= 2.6073-1.9745i \end{aligned} $$Explanation
Polynomial $ x^9-5x^8+10x^7+5x^5-x^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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