Find the product of all positive integer values of c such that \(8x^2+15x+c=0 \)has two real roots.
The discriminant must be greater than zero, so:
15^2 - 4*8*c > 0
225 - 32c > 0
This will be the case for c = 1, 2, 3, 4, 5, 6 and 7
The product is 7! → 5040