Find roots of polynomial $$ p(x) = x^7-4x^6+6x^5-4x^4+x^3-1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.6782\\[1 em]x_2 &= 0.3293+0.8433i\\[1 em]x_3 &= 0.3293-0.8433i\\[1 em]x_4 &= -0.4457+0.3793i\\[1 em]x_5 &= -0.4457-0.3793i\\[1 em]x_6 &= 1.2773+0.7012i\\[1 em]x_7 &= 1.2773-0.7012i \end{aligned} $$Explanation
Polynomial $ x^7-4x^6+6x^5-4x^4+x^3-1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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