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Problem 3 of Third round - Least value of leading coefficient

Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade

December 14, 2019
algebra

Problem Statement

Let a,b,ca,b,c be integers, a>0a>0 and the equation ax2āˆ’bx+c=0ax^2-bx+c=0 has two distinct real roots in the interval (0,1)(0,1). Find the least possible value of aa.
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