Another quadratic.
Source: INMO 1999 Problem 5
October 7, 2005
quadraticsalgebra unsolvedalgebra
Problem Statement
Given any four distinct positive real numbers, show that one can choose three numbers from among them, such that all three quadratic equations \begin{eqnarray*} Bx^2 + x + C &=& 0\\ Cx^2 + x + A &=& 0 \\ Ax^2 + x +B &=& 0 \end{eqnarray*} have only real roots, or all three equations have only imaginary roots.