Find roots of polynomial $$ p(x) = -22x^{10}+6x^5+5x^4+6x^2-2x-7 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.5337+0.7834i\\[1 em]x_2 &= 0.5337-0.7834i\\[1 em]x_3 &= -0.6214+0.7169i\\[1 em]x_4 &= -0.6214-0.7169i\\[1 em]x_5 &= 0.8497+0.1413i\\[1 em]x_6 &= 0.8497-0.1413i\\[1 em]x_7 &= 0.0195+0.9079i\\[1 em]x_8 &= 0.0195-0.9079i\\[1 em]x_9 &= -0.7815+0.1796i\\[1 em]x_{10} &= -0.7815-0.1796i \end{aligned} $$Explanation
Polynomial $ -22x^{10}+6x^5+5x^4+6x^2-2x-7 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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