JEE Quadratics problem

Algebra Level 5

Consider the quadratic equation \(ax^{2}-bx+c=0\) where \(a,b,c \in \mathbb N\) which has two distinct real real roots belonging to the interval \((1,2)\).If the least values of \(a,b,c\) are \(A,B,C\) respectively then find \(A+B+C\)

This problem is part of my set Some JEE problems.
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