Mathematician Finds Easier Way to Solve Quadratic Equations

www.popularmechanics.com ^ | Dec 6, 2019 | By Caroline Delbert

[William Tell]

"... you just divide both sides by a."

Of course.

But this does introduce an additional step.

Furthermore, the video is actually doing the general solution without realizing that it is doing so.

Note that he mentions equidistance of solutions by suggesting that the sum of the two solutions must be 8. He concludes that the solutions are (4+u) and (4-u).

He could have just as easily said that (-b/2a) is the average of the two solutions, which not surprisingly is easily calculated as, ... wait for it ..., 4.

The rest of the calculation is u = sqrt(b²-4ac)/2a or, since a=1,
u = sqrt(b²-4c)/2 = sqrt(64-48)/2 = sqrt(16)/2 = 2.

I just don't see the advantage, especially when using such simple coefficients.

Furthermore, I notice what I think is a slight weakness in his derivation. His initial assumption is that the roots are (4+u) and (4-u). He is considering u to be either positive for both roots or negative for both roots, but not both. Then he multiplies the two roots, simplifies, and recognizes that there are two solutions for u.

It works in this case, but I would be very reluctant to carry out such a calculation without some consideration of which root to use. It is possible to introduce impossible solutions with such steps. I think we have all seen the calculations that prove that 2=1 or some such contradiction by dividing by zero without recognizing it.

[HeadOn]

I’m a Mechanical Engineer, and minored in Math (MANY years ago...). I memorized multiplication tables in 3rd grade, the quadratic equation in Junior High, and many other things along the way (including some manipulations in Calculus).

THERE IS NOTHING WRONG WITH MEMORIZATION! IT WORKS! “More intuitive” is good, but I found it perfectly acceptable to be able to get answers BEFORE I completely understood the methods... After I did understand what the “mechanical” method got me, if I decided to go another way, or that I could do something more easily MY way, fine - but why do you want to screw with something that’s not any harder if it has been working for decades?

Millions of people get in a car and drive without the slightest understanding of how the vehicle works. Let’s do something “more intuitive” to teach them how to drive.

[Leaning Right]

It is also worth noting that the quadratic formula did not just mysteriously spring out of nowhere. It was logically derived from the completing the square method.

I taught algebra for quite a few years. In my mainstream classes I just presented the quadratic formula, and mentioned where it came from. Then we applied it. In my honors classes we first took the time to derive the formula.

And here’s where the field of education is different than engineering. Engineers will change things if a new way is better. Educators will change things if a new way is different. No one above the level of teacher bothers to consider if that new way is better or worse.

[HeadOn]

“Engineers will change things if a new way is better. Educators will change things if a new way is different.”

My Mom taught elementary school for 37 years, and she’s right there with you...

Not sure how to do a virtual fist bump, but consider it done. Have a great Christmas.

[Right Wing Assault]

Wait a minute! This is useless. Why, because it is wrong to tell the students to get the RIGHT answer because there are no right answers. Just pick two numbers. Or maybe three if you want. Or tell the teacher there is no correct answer.

This guy is racist. He's the one who is making black people beating of Asians. Arrest him.