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Math Genius Has Come Up With a Wildly Simple New Way to Solve Quadratic Equations:
If you studied algebra in high school (or you're learning it right now), there's a good chance you're familiar with the quadratic formula. If not, it's possible you repressed it.
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.
In a 2019 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.
"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.
[...] We still don't know how this escaped wider notice for millennia, but if Loh's instincts are right, maths textbooks could be on the verge of a historic rewriting - and we don't take textbook-changing discoveries lightly.
"I wanted to share it as widely as possible with the world," Loh says, "because it can demystify a complicated part of maths that makes many people feel that maybe maths is not for them."
The research paper is available at pre-print website arXiv.org, and you can read Po-Shen Loh's generalised explanation of the simple proof here.
(Score: 2) by KritonK on Monday July 06 2020, @04:23PM (1 child)
It is an easy way to factorize a quadratic equation, without having to remember the formula for the determinant or how to use it to calculate the roots of the equation. It is equivalent to the determinant method of calculating roots (the author proves this at the end of the article), but, unlike the determinant method, it is easier to do the calculation in your head.
As for the guess-and-check method, it's the first time I hear about it, too, but I think that he refers to cases where the equation is obviously in the form of x2 -(a+b)x + ab, which is equivalent to (x-a)(x-b), so the roots are a and b. When a and b are not obvious, one may be tempted to identify them by guessing, to avoid calculating the roots using the determinant. The author eliminates this guessing part, by describing how to calculate a and b simply, from their sum and product.
(Score: 3, Insightful) by stormreaver on Monday July 06 2020, @07:48PM
The sum-and-product method described in the article was part of my College Algebra (MTH 135) class back in the early 1990's (1992, if I remember correctly). This is neither new nor novel.