USAMO 1988 Problem 2

The cubic $x^{3}+a x^{2}+b x+c$ has real coefficients and three real roots $r \geq s \geq t$. Show that $k=a^{2}-3 b \geq 0$ and that $\sqrt{ } \mathrm{k} \leq \mathrm{r}-\mathrm{t}$.