$$x^{10}-25x+1 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.04 & x_2 = 1.42545 & x_3 = -1.34811+0.4891i \\[1 em] x_4 = -1.34811-0.4891i & x_5 = -0.71939+1.23845i & x_6 = -0.71939-1.23845i \\[1 em] x_7 = 1.09092+0.91921i & x_8 = 1.09092-0.91921i & x_9 = 0.24386+1.40831i \\[1 em] x_10 = 0.24386-1.40831i & \\[1 em] \end{matrix} $$
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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