Comment by teo_zero
7 hours 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?
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.