$$x^5-3x^3+4x^2+x-1 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.4483 & x_2 = -0.5303 & x_3 = -2.13358 \\[1 em] x_4 = 1.10779+0.86276i & x_5 = 1.10779-0.86276i \\[1 em] \end{matrix} $$
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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