Let $a,b,c $ be Natural Numbers, such that roots of the equation $ax^2+bx+c=0$ are distinct and both lie in the interval
(Brackets signify open interval, roots are $IN BETWEEN $ the numbers in each part.)
Find minimum possible value of $a, b, c.$
On my part, I solved for part 1, i.e. for distinct roots between (0,1). But for the next two parts, the things are getting a too bit messy.
While it may have similarity in question for given part 1 in stack exchange, there is no generalized method so that we can solve for other such intervals.
So please help, I am new to stack exchange.