Find roots of polynomial $$ p(x) = x^7-4x^6+6x^5-6x^4+5x^3-3x-3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 2.0358\\[1 em]x_2 &= -0.4673+0.3621i\\[1 em]x_3 &= -0.4673-0.3621i\\[1 em]x_4 &= 0.0321+1.3049i\\[1 em]x_5 &= 0.0321-1.3049i\\[1 em]x_6 &= 1.4173+0.683i\\[1 em]x_7 &= 1.4173-0.683i \end{aligned} $$Explanation
Polynomial $ x^7-4x^6+6x^5-6x^4+5x^3-3x-3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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