$$x^6+x^4-216x^3+x^2+1 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.16827 & x_2 = 5.94283 & x_3 = -0.08182+0.14429i \\[1 em] x_4 = -0.08182-0.14429i & x_5 = -2.97373+5.24421i & x_6 = -2.97373-5.24421i \end{matrix} $$
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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