$$5x^6-3x^2+7 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.91852+0.44226i & x_2 = 0.91852-0.44226i & x_3 = -0.91852+0.44226i \\[1 em] x_4 = -0.91852-0.44226i & x_5 = 1.1385i & x_6 = -1.1385i \end{matrix} $$
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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