$$x^5-4x^4+7x^2-9 = 0$$
Answer
$$ \begin{matrix}x_1 = 3.48453 & x_2 = 1.26379+0.63062i & x_3 = 1.26379-0.63062i \\[1 em] x_4 = -1.00605+0.53162i & x_5 = -1.00605-0.53162i \\[1 em] \end{matrix} $$
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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