+1678 Can anyone help?
Find the product of all positive integer values of $c$ such that $8x^2+15x+c=7x^2-20x+8$ has two real roots.
+130071 8x^2 + 15x + c = 7x^2 -20x + 8 rearrange as
x^2 + 35x + (c - 8) = 0
To have two real roots, the discriminant must be > 0
So
35^2 - 4(1) (c - 8) > 0
1225 - 4c + 32 > 0
1257 - 4c > 0
1257 > 4c
4c < 1257
c < 1257 / 4 = 314.5
So...any integer c < 314.5 will work
And since c must be a positive integer c = 1 * 2 * 3 * 4 * .....* 312 * 313 * 314
So....the product of all integer c's = 314! [ a really BIG number !!!!!]
