Find the product of all positive integer values of c such that \(8x^2+15x+c=0\) has two real roots.
If this has two real roots, then the discriminant must be > 0
So
15^2 - 4(8)c > 0
225 - 32c > 0
225 > 32c
c < 225/32 ⇒ c < 7.03125
So....the positive integer values for c that produce two real roots are [ 1, 7 ]
And their product = 7! = 5040