![po shen loh po shen loh](https://arc-anglerfish-washpost-prod-washpost.s3.amazonaws.com/public/7FDEQSGRIY73TD3IDR5N5IDOWI.jpg)
All we need to do is to find if there exists a u such that 1 + u and 1 − u work as the two numbers, and u is allowed to be 0."Īccording to Loh, a valid value for u can always be determined per Loh's alternative quadratic method, in an intuitive way, making it possible to solve any quadratic equation.
#Po shen loh plus
"So, we can try to look for numbers that are 1 plus some amount, and 1 minus the same amount. "The sum of two numbers is 2 when their average is 1." Loh explains on his website. He uses an averaging technique that concentrates on the sum, as opposed to the more commonly taught way of focusing on the product of two numbers that make up c, which requires guesswork to solve problems. In Loh's new method, he starts from the standard method of trying to factor the quadratic x² + bx + c as (x − )(x − ), which amounts to looking for two numbers to put in the blanks with sum −b and product c. "How can it be that I've never seen this before, and I've never seen this in any textbook?" "I was dumbfounded," Loh says of the discovery. In September, Loh was brainstorming the mathematics behind quadratic equations when he struck upon a new, simplified way of deriving the same formula – an alternative method which he describes in his paper as a "computationally-efficient, natural, and easy-to-remember algorithm for solving general quadratic equations". That formula can be used to solve standard form quadratic equations, where ax 2 + bx + c = 0. Of course, there have always been alternatives to the quadratic formula, such as factoring, completing the square, or even breaking out the graph paper.īut the quadratic formula is generally regarded as the most comprehensive and reliable method for solving quadratic problems, even if it is a bit inscrutable. That arduous task – performed by approximately four millennia worth of maths students, no less – may not have been entirely necessary, as it happens. "It is unfortunate that for billions of people worldwide, the quadratic formula is also their first (and perhaps only) experience of a rather complicated formula which they must memorise," Loh writes. In a new research paper, Loh celebrates the quadratic formula as a "remarkable triumph of early mathematicians" dating back to the beginnings of the Old Babylonian Period around 2000 BCE, but also freely acknowledges some of its ancient shortcomings.
![po shen loh po shen loh](http://ocscholar.org/images/Math/GuestLecture1.jpg)
By this point, billions of us have had to learn, memorise, and implement this unwieldy algorithm in order to solve quadratic equations, but according to mathematician Po-Shen Loh from Carnegie Mellon University, there's actually been an easier and better way all along, although it's remained almost entirely hidden for thousands of years.