Mathematics in the tree snakes

(2003 korea SAT)
There is a cubic equation   for x.
To have a separate three real root of an integer n is the number?

Bar (n) to the intersection point that there will be three snakes f (x) the touch.
Venom subtract, f(x) snake can be drawn.
Subtracting venom is the differential.

Thus, a 31 fold the number of integers that satisfy.