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.