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1988 USAMO Problem 2

Source:

July 27, 2011
AMCUSA(J)MOUSAMOalgebrapolynomialVietaalgebra unsolved

Problem Statement

The cubic equation x3+ax2+bx+c=0x^3 + ax^2 + bx + c = 0 has three real roots. Show that a2−3b≥0a^2-3b\geq 0, and that a2−3b\sqrt{a^2-3b} is less than or equal to the difference between the largest and smallest roots.
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