Comment by teo_zero
6 months ago
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.