Find the product of all positive integer values of c such that \(8x^2+15x+c=0\) has two real roots.
+128474 8x^2 + 15x + c = 0
This will nave two real roots if
15^2 - 4 * 8 * c > 0
225 - 32c > 0
225 > 32c
225/ 32 > c
7.03125 > c
So......c will have two real roots [and be positive ] for all integer values from 1 to 7, inclusive
And the procuct of these possible values for c = 7! = 5040
