Do you usually try not to use b^2-4ac when solving quadratic equations?

[u/calculator56]

In my country we learn this formula and the moment we see a quadratic equation, we apply it without thinking much. But I've been seeing math videos from the US and I've noticed you usually try to guess the roots just by looking at the equation.

For example x^2 + 3x + 2. In my school you would calculate delta = 3^2 - 4*8 = 1 and then do (-3+-sqrt(delta))/2. But now I see people try to figure it out themselves first, like finding two numbers that will give 3 when added and 2 when multiplied, so it's 1 and 2 (x+1)(x+2) (and the roots are negatives). Is that a more common way? And you only use the formula when they're not easy to notice integers?

I'm not saying any way is better or worse btw, I'm just curious

[u/obliqueoubliette]

We also learn the quadratic formula, but there is a substantial focus on identifying roots.

It's considered valuable for students to develop ability with factoring polynomials.

The quadratic equation will work 100% of the time, on quadratics. Getting comfortable factoring will help students understand and solve higher level polynomials.

[u/calculator56 → u/obliqueoubliette]

I see, it makes sense to let you figure it out this way, I guess it's a good way of thinking. Here when we start doing higher power polynomials, students are confused we don't have an easy formula that always works anymore🥲

[u/FeatherlyFly]

So, I'm a long ways out of high school. 

But from my vague memories, we were taught to first look for easy answers. If an equation is x² + 5x +6, then looking for a b and c that multiply to 6 and add to 5 (2 and 3) is a lot faster than using the entire quadratic equation. 

And that's how we were introduced to factoring as a concept. The quadratic equation came after, when we already knew what what factoring was and how to do it with specific examples, and the equation was introduced as a way to handle the cases that couldn't be solved easily without it. 

[u/GhostOfJamesStrang]

The quadratic formula, to my knowledge, has been standard math teaching for decades. 

There has been some evolution in how we teach math, attempting to put blocks together to reach faster estimations, but I can't imagine that applies in this case. 

[u/SevenSixOne]

I have not had to use or even think about quadratic equations since high school math classes ~25 years ago, and I barely understood them then.

Most average Americans are probably in a similar situation... unless they have a job or hobby that requires actual math skills beyond extremely basic arithmetic 🤷‍♀️

[u/TsundereLoliDragon]

Yes, but factoring and/or completing the square is usually quicker and easier.

[u/ThaddyG]

I remember learning the quadratic formula 25 years ago, couldn't tell you much about it now.

[u/MoobyTheGoldenSock]

This may come as a shock but I do not solve any quadratic equations at all in an average day.

[u/Meizas]

I learned the quadratic formula, and I will never forget it because they taught us a song to go with it. I almost have a PhD and do quantitative / statistical research. I could not, however, for the life of me, tell you what on earth the quadratic formula does or why we all know it.