It depends on how many different roots the equation has.

Observe that between any 2 different roots that attains a maximum/minimum in the interval .

And there exists a with where the tangent at passes through the origin.

But we might just as well calculate how many maxima/minima f(x) attains:

Thus if you find all different "real " roots of you're done.

Edit: You don't even have to find the roots of explicitly. You can use the intermediate value theorem to decide how many roots in this equation has.