1988 USAMO Problems/Problem 2

Problem

The cubic polynomial $x^3+ax^2+bx+c$ has real coefficients and three real roots $r\ge s\ge t$ . Show that $k=a^2-3b\ge 0$ and that $\sqrt k\le r-t$ .

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1988 USAMO (Problems • Resources)
Preceded by Problem 1	Followed by Problem 3
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