Find roots of polynomial $$ p(x) = x^6-2x^5-2x^4+2x^3+2x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.4142\\[1 em]x_2 &= -1.272\\[1 em]x_3 &= 1.272\\[1 em]x_4 &= 2.4142\\[1 em]x_5 &= 0.7862i\\[1 em]x_6 &= -0.7862i \end{aligned} $$Explanation
Polynomial $ x^6-2x^5-2x^4+2x^3+2x+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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