The value of the function when x=0 is called the y-intercept. It is the place where the function crosses the y-axis. This is the point (0,ab).
Put x=0 into the expression and get ab.
Now, the "solutions" of (x=-a) and (x=-b) result from the Multiplicative Property of Zero (if the product is zero, then at least one of the factors must be 0).