A geometric method for solving quadratic equations

King Shun LEUNG, Ka Wo CHAN

Research output: Contribution to conferencePaper

Abstract

The theory of quadratic equations (with real coefficients) is an important topic in the secondary school mathematics curriculum, including the current DSE curriculum in Hong Kong. Usually students are taught to solve a quadratic equation ax² + bx + c = 0 ( a ≠ 0 ) algebraically (by factorisation, completing the square and using the quadratic formula), graphically (by plotting the graph of the quadratic polynomial y = ax² + 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. In this workshop we are going to describe this approach. However, the tool we use is a set square rather than a ruler and a compass, which are the traditional tools employed in geometric construction. We choose a set square because it is more convenient (one tool is used instead of two). Surely the methods to be presented in the workshop can also be carried out in the traditional manner. It is also worth mentioning that any construction done with a ruler and a compass can also be done with a set square, though the underlying geometric theorems may be different. Of course, we cannot draw a circle with a set square. But we can locate as many points as we wish on the circumference of a circle with given centre and radius. We hope that school teachers can incorporate some of the ideas in the design of learning activities for their students.
Original languageEnglish
Publication statusPublished - Jun 2017

Fingerprint

Set square
Quadratic equation
Ruler
Completing the square
Quadratic equation solution
Circle
Geometric theorem
Bisection Method
Newton-Raphson method
Circumference
Quadratic Polynomial
Intercept
Factorization
Choose
Radius
Coefficient
Graph in graph theory

Citation

Leung, K. S., & Chan, K. W. (2017, June). A geometric method for solving quadratic equations. Paper presented at the 2017 Hong Kong Mathematics Education Conference, The Education University of Hong Kong, Hong Kong.