If the three real zeros of a function f(x) are located at x = r, x = q, and x = p, determine (if possible) the?

Think about all the types of functions. Will multiplying a polynomial by a constant change its roots or just cause it to shrink? What about rational functions and trigonometric functions? Also, what sort of functions can have three roots at all? Exponential, logarithmic, polynomial, trigonometric?