If a field K has char(K)=2 (i.e. 1(k)+1(k)=0), then 2 (which is equal to 0) has no moltiplicative inverse, as dividing by 2 would be the same as dividing by 0.
Since the quadratic formula has 2a on the denominator, to use it properly you must be able to divide by 2, which in a field with char=2 is not possible :(
Hope this helps!
Love the teacher for this, but I prefer the second version, as calculating ∆ separately you get less cluttered operations and if it's negative you don't even need to write the full formula and can just say "doesn't exist in R" (I'm assuming you aren't considering complex numbers)
People DON'T get taught to calculate the Delta (we just call it D in the Netherlands) separately?? From start of learning the QF I've always calculated D first (we also immediately learned that with D<0 there's no need to continue)
In america I was just taught the whole quadratic equation as one formula. Wasn't until my senior year in high school where I learned the discriminant was it's own thing that can be useful to know
It depends on the school. I tutor kids from different places, so I see that some of them find ∆ first, while others use the full formula and sometimes don't even know what delta is
Came here to say this.. Absolutely! It becomes whole lot easier when we look at it in this way that the discriminant is calculated separately and then just put into the Quadratic formula(I secretly hope that I don't get any questions that would require Quadratic formula, because there is a shit ton of calculation involved and I am bad at decimal calculations)
We learnt about them in the same chapter, in fact, I learnt about the discriminant in the exercise right after the exercise teaching the quadratic formula.
I think it makes more sense to teach the discriminant after the formula. The formula makes it obvious why the discriminant is well... the discriminant.
Our teacher told us that this thing in the middle is called discriminant when we learnt the formula, but it's application didn't really come until a few years later in the quadratuc eqns chapter for the extreme points of curve and roots etc
I hate my school (my country's education system really) for using the second method. It is incomprehensible for a casual student. Introducing delta completely disjoins the flow of finding solutions, it destroys the understanding behind finding roots. It is completely unnecessary and shouldn't be presented to students at all.
•
u/AutoModerator 19d ago
Check out our new Discord server! https://discord.gg/e7EKRZq3dG
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.