This article describes three different approaches to finding the roots of an algebraic equation and concludes with a set of heuristics for solving equations in general. Our principal example is an earlyround elimination problem from the 1939 Moscow Mathematical Olympiad for students in grades 11 and 12 (Shklarsky 1993, problem 168). As we tell our students, you will get much more out of a problem if you work on it for 15 to 20 minutes and fail than if you turn to the solution after only 3 minutes.
Michael Stueben, Michael.Stueben@fcps.edu, teaches precalculus and computer science at Thomas Jefferson High School for Science and Technology, Alexandria, VA 22312, and is the author of Twenty Years before the Blackboard. He is currently interested in applying the Moore method of teaching high school students.
Shane Torbert, Shane.Torbert@fcps.edu, teaches mathematics and computer science at Thomas Jefferson High School for Science and Technology. He is interested in creativity and imagination in problem solving.