JEE Quadratics problem

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 .