## Challenge 264: Quadratic Query

The values of x which solve the quadratic equation x^{2} + px + 1 = 0 are a and b.

The values of x which solve the quadratic equation x^{2} + qx + 1 = 0 are c and d.

What is the value of (a + c)(b + c)(a – d)(b – d) if p = q?

More generally, what is the value of (a + c)(b + c)(a – d)(b – d) in terms of p and q?