[This is really a Calculus question, it doesn't belong in the Algebra section.]

If then f(3) and f(4) have different signs, so f must have a zero somewhere between 3 and 4 (that's because of the intermediate value theorem, which you probably ought to know).

Also, f(4)>0, and if you differentiate f you'll find that the derivative is positive whenever x>4. So f(x) is increasing for x>4 and so it can never decrease down to 0 again.