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Part of 1969 Polish MO Finals

Problems(1)

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

Source: Polish MO Finals 1969 p1

Prove that if real numbers

a,b,c

satisfy the equality

\frac{a}{m+2}+\frac{b}{m+1}+\frac{c}{m}= 0

for some positive number

m

, then the equation

ax^2 + bx + c = 0

has a root between

0

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