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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 Immerman on Tuesday July 07 2020, @03:25PM
Did they stop?
Seems like I, and everyone I've tutored over the years, got the basic factorization first. It's just that it's only a brief conceptual step of "reversing the FOIL method" to figure out the solution, which is very rapidly skipped over in favor of the quadratic formula, since manual factorization is mostly useless in the real world.
If it weren't for the fact that there is no general formula to solve for cubic and higher-order equations I'd question the value of teaching mostly-useless manual factorization at all. As it is though, manual factorization is an unavoidable evil in solving higher-order polynomial equation, and comes in handy for symbolic solutions in trig, calculus, etc., so at least the practice doesn't go completely to waste.