Yeah I tried deriving it and doing a little algebra work and I'm just going around in circles, I don't get it.
One thing though, when x approaches 1
A(1)2 + B(1) + C = 0
A + B + C = 0, smallest possible positive number
So, you could half ass it and say x=0.9999... and C=0
Then A and B are super small as well, you get the smallest possible number.
So A, B and C approach (or are) 0, X approaches 1 to get the smallest number.