$$x^5+3x^4-7x^3+4x^2+x+1 = 0$$
Answer
$$ \begin{matrix}x_1 = -4.67332 & x_2 = -0.17563+0.35316i & x_3 = -0.17563-0.35316i \\[1 em] x_4 = 1.01228+0.59227i & x_5 = 1.01228-0.59227i \\[1 em] \end{matrix} $$
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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