Let a,b,c be nonzero perfect squares such that b=a+c. The equation ax2−bx+c=0 has the following properties:
- It has a real root d that is greater than 1. (The other root may or may not be real.)
- The square root of the quadratic discriminant is a prime number.
Among all such (a,b,c,d), pick the one such that the discriminant is minimum. Find abcd.