We should not be doing your homework. But since Star has already answered your question, let me see if I can give you an idea. (And Star did not answer your question in a way that is probably useful, since calling fzero might be a flaw for a homework assignment.)
If a function is continuous over an entire interval, and it has a sign that changes from one end of the interval to the other, then does it cross zero, at SOME unspecified point in the interval? In fact, the function may have more than one solution on that interval. But it is sufficient to test the end points of the interval, and to verify the function is finite and continuous everywhere on that interval.
In fact, this is virtually one of the first things that fzero does test when called with an interval on some general function. If there is no sign change, then it generates an error. In fact, that is not sufficient to insure the existence of a root, since if the function is discontinuous, then no root actually needs to exist.
