Mathematician discovers a simpler way to solve the quadratic equation

Mathematician discovers a simpler way to solve the quadratic equation that could fundamentally change the way students are taught math

  • A professor at Carnegie Mellon found a new way to solve the quadratic equation
  • The new method avoids the traditional ‘guess and check’ method currently in use
  • He came up with the new approach while coaching for the USA Math Olympiad

In a boon to algebra students everywhere, a professor at Carnegie Mellon University has devised a simpler and more efficient way to solve problems involving the quadratic equation.

The new method was devised by Dr. Po-Shen Loh while he was trying to think up some test problems involving quadratic equations for the junior high school students he coaches for the USA Math Olympiad.

Loh’s method involves applying a much simpler equation to solve for one of the variables in the quadratic equation without having to go through with the often messy and confusing calculations of the full equation.

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The quadratic equation (pictured above) is one of the main concepts in early algebra, and one that can be consistently confusing to new students

‘I was dumbfounded,’ Loh said in a video explaining his discovery, reported by Popular Mechanics.

‘How can it be that I’ve never seen this before and I’ve never seen this in any textbook?’

Initially, Loh couldn’t believe he had been the first to discover his new method and he went back deep into history to double check old Babylonian and Indian math texts.

Part of what makes the quadratic equation so difficult is that it has not one answer, but two, something that’s called a ‘polynomial’ equation in math lingo.

Because students trying to solve the equation have to make sure their answers work for two different numbers, most end up resorting to a labor intensive guess and check method, in which students would plug numbers into the equation to see if they’d work.

For Loh, there was something about this process that ran counter to spirit of math, which was supposed to be about making ‘something that was supposed to be complicated into something simple.’

In the typical quadratic equation–X2 – BX + C = 0—students would try and solve for the two different values of X using a rule of thumb: The value of B should equal the sum of Xs two different values, and C should be what you get when you multiply the two values of X together.

Dr. Po-Shen Loh of Carnegie Mellon University (pictured above) stumbled on a simpler secondary equation that allows students to accurately solve quadratic equations without having to deal with the labor-intensive and imprecise ‘guess and check’ method

WHAT IS THE QUADRATIC EQUATION? 

The quadratic equation is an ancient staple of mathematics that dates back to ancient Babylonians in 2000 BC.

 It was originally devised as a way to help calculate problems involving rectangles whose sides might vary in length.

It’s a ‘polynomial equation,’ meaning that it always has two valid solutions.

Most students currently learn to solve using the ‘guess and check’ method, where they make an educated guess about what range the answer might fall into and then calculate whether their guess actually works. 

This rule gave students a general framework to begin guessing at what potential number combinations might fit for X, but Loh realized that there was a second, simpler equation that could be used to solve for B that would make all the other guess work irrelevant.

‘Because this method solves the problem by starting from the sum, it can be used to solve any quadratic equation,’ Loh says.

‘I wanted to share it as widely as possible with the world because it can demystify a complicated part of math that makes many people maybe feel like math is not for them.’

‘I think that if one can show that mathematics is actually a subject that is still alive in a way that every single person can appreciate, this is a benefit.’

 

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