Find roots of polynomial $$ p(x) = x^{10}-5x^9+10x^8-10x^7+5x^6-x^5+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.5+0.866i\\[1 em]x_2 &= 0.5-0.866i\\[1 em]x_3 &= -0.5654+0.2759i\\[1 em]x_4 &= -0.5654-0.2759i\\[1 em]x_5 &= -0.1685+0.7113i\\[1 em]x_6 &= -0.1685-0.7113i\\[1 em]x_7 &= 1.1685+0.7113i\\[1 em]x_8 &= 1.1685-0.7113i\\[1 em]x_9 &= 1.5654+0.2759i\\[1 em]x_{10} &= 1.5654-0.2759i \end{aligned} $$Explanation
Polynomial $ x^{10}-5x^9+10x^8-10x^7+5x^6-x^5+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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