What’s wrong with the Quadratic Formula?
Let me count the ways:
- It’s pure magic to 99% of high-school students, who have no idea why it works.
- It lends itself to sign errors because of the subtraction under the square root sign. When you subtract a negative, you get something unpredictable.
- It lends itself to order-of-operation errors because too many people forget to multiply before they subtract.
- Finally, too many people forget to calculate the entire numerator before dividing by 2a, so they end up only dividing the radical by 2a.
OK, so what about factoring? Surely that avoids all three of these problems.
Well, maybe, but it has problems of its own, as explained in a recent article that discussed a new-but-old improved way to solve quadratic equations. The article is by one Caroline Delbert, presumably a staffer for Popular Mechanics, but the content is all by a distinguished mathematician, Dr. Po-Shen Loh at Carnegie Mellon University. Read the article and/or watch the video.
Note that Dr. Loh explains the historical antecedents of his preferred method; he isn’t claiming to have invented it. It’s a perfectly good way to solve certain quadratics, as he claims. But it only works with a very narrow subset of quadratic equations, ones that are factorable over the integers and have an initial coefficient of 1. This is a reasonably good starting point, but it’s no more than that. I’m not convinced that it’s worth all the fuss.