# Tartaglia cubic roots problem

$x=\sqrt[3]{q+\sqrt{q^2-p^3}}-\sqrt[3]{-q+\sqrt{q^2-p^3}}$

Why is it that this must be true $q^2-p^3<0$ for x to have 3 distinct real roots?

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Do you mean $q^2−p^3<0$? Square roots are always positive. –  lhf Sep 17 '12 at 20:56
Yes, sorry- will adjust. –  Alyosha Sep 19 '12 at 18:59