$$3x^6-22x^4+31x^2-1 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.18174 & x_2 = -0.18174 & x_3 = -1.36108 \\[1 em] x_4 = 1.36108 & x_5 = 2.33404 & x_6 = -2.33404 \end{matrix} $$
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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