2 Values of x, where f(x) = 0 (Single-Var Calc)

Find 2 values of x that make f(x) = 0.

f(x) = (x-a)(x-b)(x-c)

The obvious answers are x = {a, b, c}, but considering this is a calculus class where he usually assigns pretty challenging homework there must be another solution. There are 2 more parts to the question if it will help you understand where hes heading:

2. Find the average of the two values of x you found above. What point on the graph of f has this x-value?

3. Find the equation for the tangent line at the point you found above, and find all points where the tangent line intersects the graph y = f(x), where f is defined above.

I don't want to be given the answers, but I would like some sort of recommendation on how to address the problem.

Thanks for any help in advance.