I teach math in the first year of the university in Argentina. This method is well known since many years, probably like 20 or more. It's more popular in foreign students (Brazil? Peru?) that have some kind of standardized test with many short questions. The local students use the classic formula (sometimes unsuccessfully).
It's a nice trick for equations with small nice numbers, that are common in math tests. But it fails spectacularly when you try to apply it to physics or chemistry problems that have decimals and nasty irrational solutions.
I don't like it, because it use that mathematicians like to put only nice numbers, even in topics like linear algebra or calculus that are about the real numbers.
But I don't mind something like this method for advanced math courses like Galois Theory, where the polynomials have integer or rational coefficients, and you can use the Gauss method https://en.wikipedia.org/wiki/Rational_root_theorem to find all the rational roots, that is quite similar to this "new" method.
This works nicely as long as the leading coefficient is 1. But then, the quadratic formula reduces to (-b +/- sqrt(b^2-4c) / 2)... which is the same amount of calculation.
I don't get it. Isn't this exactly how the well-known formula is constructed? (With the example crafted to have integers, even solutions and a=1 so to conveniently hand-wave the last division.)
> Normally, when we do a factoring problem, we are trying to find two numbers that multiply to 12 and add to 8. Those two numbers are the solution to the quadratic, but it takes students a lot of time to solve for them, as they’re often using a guess-and-check approach.
Wait... don't students apply the closed-form formula? Do we teach them that maths is about guessing? Next what? that pi is a rational number equal to 22/7, maybe?
80% of solving mathematics problems is guessing. You are not required to guess only in situations where you know what formula to apply/how to proceed because the teacher told you to or the problem is trivial. You guess the steps, try them, try another guess if the first one does not work, then you iron out the special cases if any and make the whole proof rigorous.
It's not a different way to solve quadratic equations, but a derivation of the traditional formula that has intermediate steps filled in instead of leaving them as an exercise for the reader. This is probably mostly relevant when the reader is a slightly incompetent teacher who ends up bungling the intermediate steps and transfers their confusion on to unsuspecting students.
I teach math in the first year of the university in Argentina. This method is well known since many years, probably like 20 or more. It's more popular in foreign students (Brazil? Peru?) that have some kind of standardized test with many short questions. The local students use the classic formula (sometimes unsuccessfully).
It's a nice trick for equations with small nice numbers, that are common in math tests. But it fails spectacularly when you try to apply it to physics or chemistry problems that have decimals and nasty irrational solutions.
I don't like it, because it use that mathematicians like to put only nice numbers, even in topics like linear algebra or calculus that are about the real numbers.
But I don't mind something like this method for advanced math courses like Galois Theory, where the polynomials have integer or rational coefficients, and you can use the Gauss method https://en.wikipedia.org/wiki/Rational_root_theorem to find all the rational roots, that is quite similar to this "new" method.
It would be far better if the actual blog post was posted instead of Popular Mechanics' summary.
https://www.poshenloh.com/quadratic/
This works nicely as long as the leading coefficient is 1. But then, the quadratic formula reduces to (-b +/- sqrt(b^2-4c) / 2)... which is the same amount of calculation.
I don't get it. Isn't this exactly how the well-known formula is constructed? (With the example crafted to have integers, even solutions and a=1 so to conveniently hand-wave the last division.)
> Normally, when we do a factoring problem, we are trying to find two numbers that multiply to 12 and add to 8. Those two numbers are the solution to the quadratic, but it takes students a lot of time to solve for them, as they’re often using a guess-and-check approach.
Wait... don't students apply the closed-form formula? Do we teach them that maths is about guessing? Next what? that pi is a rational number equal to 22/7, maybe?
80% of solving mathematics problems is guessing. You are not required to guess only in situations where you know what formula to apply/how to proceed because the teacher told you to or the problem is trivial. You guess the steps, try them, try another guess if the first one does not work, then you iron out the special cases if any and make the whole proof rigorous.
It's not a different way to solve quadratic equations, but a derivation of the traditional formula that has intermediate steps filled in instead of leaving them as an exercise for the reader. This is probably mostly relevant when the reader is a slightly incompetent teacher who ends up bungling the intermediate steps and transfers their confusion on to unsuspecting students.
Feels a little weird, given that there is an easy closed formula for the solutions.
Nice one! I will be using this.
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