HMMT November 2015 U22

Find all the roots of the polynomial $x^{5}-5 x^{4}+11 x^{3}-13 x^{2}+9 x-3$ .

Dataset text NuminaMath olympiads. Quoted with source.

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1, \frac{3+\sqrt{3} i}{2}, \frac{1-\sqrt{3} i}{2}, \frac{3-\sqrt{3} i}{2}, \frac{1+\sqrt{3} i}{2}

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