$$2x^6+8x^2-1 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.35287 & x_2 = 0.35287 & x_3 = -0.9853+1.0164i \\[1 em] x_4 = -0.9853-1.0164i & x_5 = 0.9853+1.0164i & x_6 = 0.9853-1.0164i \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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