Discovering A New Way To Solve Quadratic Equations

Quadratic equations are a defining moment for many Algebra courses, and probably a source of memories of frustration for some of us! For Lamine, Grade 9 student at IST, through quadratic equations he found inspiration and a new appreciation for learning and teaching!

A quadratic equation is an equation that can be rearranged to the form: ax2 + bx + c = 0 . Quadratic equations are very important because of their versatility. By adding more powers (x2,x3,x4..) and adjusting factors, you can use quadratic equations to represent a lot of shapes mathematically. They are especially used to perform calculations on conical sections (circles, ellipses, parabolas, e.t.c).

As Lamine's class was going through the Algebra course featuring these equations, he came across an article online that piqued his interest. The article was talking about a new, much simpler way to solve quadratic equations discovered by Po-Shen Loh, an associate professor of mathematics at Carnegie Mellon University and the national coach of the United States' International Math Olympiad team.

Equation 1 - The common quadratic equation solution

 

Equation 2 -The new solution

Equation 1 is the standard solution for a quadratic equation. Equation 2 is the new method by Po-Shen Loh. Although very similar, one fundamental change makes the newer method much easier and consistent than the standard method. Instead of trying to find factors by guessing what numbers would give you the product a*c and the sum b, you instead start from average, i.e (number1+number2)/2 = b/2. This article explains the difference in detail. You can read the full paper here.

When Lamine learned about this new method, he told his teacher, Ms. Payne, who suggested he share it with the class. With Ms. Payne's help, Lamine prepared and conducted a mini-lesson about this new method. He walked his class on how to derive the equation - equation 2. And how to use it.

Through sharing and discussing this new method, Lamine helped solidify his understanding while sharing a mathematical discovery with the class!

 

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