$$x^4+2x^2+x+1 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.34381+0.62536i & x_2 = -0.34381-0.62536i & x_3 = 0.34381+1.35843i \\[1 em] x_4 = 0.34381-1.35843i & \\[1 em] \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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