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Challenge 264: Quadratic Query

The values of x which solve the quadratic equation x2 + px + 1 = 0 are a and b.

The values of x which solve the quadratic equation x2 + 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?

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