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1/2*a*x^2 + bx + c = 0

Source: IMO Longlist 1989, Problem 77

September 18, 2008
algebra unsolvedalgebra

Problem Statement

Let a,b,c,r, a, b, c, r, and s s be real numbers. Show that if r r 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 r r and s. s.