In this article, the author proves a theorem about polynomial zeros, but the focus is on how the theorem is integrated into a QuickBASIC computer program, and how that program answers the questions of the theorem--a unification of mathematics and computer programming. For a given polynomial, how can one overcome assorted problems in finding zeros and displaying graphs properly? How might a program immediately and automatically choose a domain interval? The Zero-Bounds Theorem, although not new, is not well known and the author seeks to develop a program that investigates: given a polynomial, what are its real zeros, and what does its graph look like? The computer program in QuickBASIC utilizes the theorem to search the resulting interval for zeros and to graph the function within typical limits of computer precision/accuracy. Also included is a discussion of possible shortcomings, improvements, and new research questions.