Approaching quadratic equations from a right angle. Issue 552 (16th October 2017)

• Record Type: Journal Article
• Authors: Leung, King-Shun
• Is Part Of: Mathematical gazette. Volume 101:Issue 552(2017)
• Page Start: 424
• Page End: 438
• Publication Date: 2017-10-16
• Subjects: Mathematics -- Periodicals; Mathématique; Mathematik; Mathematics; Periodicals; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); Zeitschrift; Online-Publikation; 510
• DOI: 10.1017/mag.2017.124
• Languages: English
• ISSNs: 0025-5572

Abstract

Abstract : The theory of quadratic equations (with real coefficients) is an important topic in the secondary school mathematics curriculum. Usually students are taught to solve a quadratic equation ax 2 + bx + c = 0 ( a ≠ 0) algebraically (by factorisation, completing the square, quadratic formula), graphically (by plotting the graph of the quadratic polynomial y = ax 2 + bx + c to find the x -intercepts, if any), and numerically (by the bisection method or Newton-Raphson method). Less well-known is that we can indeed solve a quadratic equation geometrically (by geometric construction tools such as a ruler and compasses, R&C for short). In this article we describe this approach. A more comprehensive discussion on geometric approaches to quadratic equations can be found in [1]. We have also gained much insight from [2] to develop our methods. The tool we use is a set square rather than the more common R&C. But the methods to be presented here can also be carried out with R&C. We choose a set square because it is more convenient (one tool is used instead of two).