$$x^6+x^4-115x^3+x^2+1 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.20871 & x_2 = 4.79129 & x_3 = -0.10001+0.17796i \\[1 em] x_4 = -0.10001-0.17796i & x_5 = -2.39999+4.27063i & x_6 = -2.39999-4.27063i \end{matrix} $$
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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