Find roots of polynomial $$ p(x) = x^8-4x^6+2x^4+4x^2-2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.6945\\[1 em]x_2 &= -0.6945\\[1 em]x_3 &= 1.2319\\[1 em]x_4 &= -1.7123\\[1 em]x_5 &= -1.2319\\[1 em]x_6 &= 1.7123\\[1 em]x_7 &= 0.9653i\\[1 em]x_8 &= -0.9653i \end{aligned} $$Explanation
Polynomial $ x^8-4x^6+2x^4+4x^2-2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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