$$4x^4+2x^3-5x^2+3x+1 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.23593 & x_2 = -1.55083 & x_3 = 0.64338+0.51896i \\[1 em] x_4 = 0.64338-0.51896i & \\[1 em] \end{matrix} $$
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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