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 would be far better if the actual blog post was posted instead of Popular Mechanics' summary.
https://www.poshenloh.com/quadratic/
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?
Feels a little weird, given that there is an easy closed formula for the solutions.
Nice one! I will be using this.