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