Indian Mathematical Olympiad 1990 - Problem 1
Source:
August 16, 2009
algebra proposedalgebraequation
Problem Statement
Given the equation
x^4 \plus{} px^3 \plus{} qx^2 \plus{} rx \plus{} s \equal{} 0
has four real, positive roots, prove that
(a) pr \minus{} 16s \geq 0
(b) q^2 \minus{} 36s \geq 0
with equality in each case holding if and only if the four roots are equal.