Find roots of polynomial $$ p(x) = x^6+100x^4-1000x^2-1000 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -3.1623\\[1 em]x_2 &= 3.1623\\[1 em]x_3 &= 0.9575i\\[1 em]x_4 &= -0.9575i\\[1 em]x_5 &= 10.4443i\\[1 em]x_6 &= -10.4443i \end{aligned} $$Explanation
Polynomial $ x^6+100x^4-1000x^2-1000 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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