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min a such that ax^2 - bx + c has two distinct zeros in the interval (0,1)

Source: 1979 Swedish Mathematical Competition p5

March 26, 2021
algebratrinomial

Problem Statement

Find the smallest positive integer aa such that for some integers bb, cc the polynomial ax2āˆ’bx+cax^2 - bx + c has two distinct zeros in the interval (0,1)(0,1).
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