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a/(m+2) + b/(m+1)+ c/m=0

Source: Polish MO Finals 1969 p1

August 22, 2024
algebra

Problem Statement

Prove that if real numbers a,b,ca,b,c satisfy the equality am+2+bm+1+cm=0\frac{a}{m+2}+\frac{b}{m+1}+\frac{c}{m}= 0 for some positive number mm, then the equation ax2+bx+c=0ax^2 + bx + c = 0 has a root between 00 and 11.
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