1/2*a*x^2 + bx + c = 0
Source: IMO Longlist 1989, Problem 77
September 18, 2008
algebra unsolvedalgebra
Problem Statement
Let and be real numbers. Show that if is a root of ax^2\plus{}bx\plus{}c \equal{} 0 and s is a root of \minus{}ax^2\plus{}bx\plus{}c \equal{} 0, then \frac{a}{2} x^2 \plus{} bx \plus{} c \equal{} 0 has a root between and