Find roots of polynomial $$ p(x) = 6x^8-16x^6-5x^4+5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.7924\\[1 em]x_2 &= 0.7924\\[1 em]x_3 &= 1.7084\\[1 em]x_4 &= -1.7084\\[1 em]x_5 &= 0.3423+0.7464i\\[1 em]x_6 &= 0.3423-0.7464i\\[1 em]x_7 &= -0.3423+0.7464i\\[1 em]x_8 &= -0.3423-0.7464i \end{aligned} $$Explanation
Polynomial $ 6x^8-16x^6-5x^4+5 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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