$$x^4+x^3+x^2+x+1 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.30902+0.95106i & x_2 = 0.30902-0.95106i & x_3 = -0.80902+0.58779i \\[1 em] x_4 = -0.80902-0.58779i & \\[1 em] \end{matrix} $$
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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