Can you prove the quadratic formula for finding roots for a general polynomial ax^2+bx+c=0?

(N.B. I ask this only because so many people are happy to throw the formula about without any real understanding of what it's doing)

Question

Can you prove the quadratic formula for finding roots for a general polynomial ax^2+bx+c=0?

(N.B.  I ask this only because so many people are happy to throw the formula about without any real understanding of what it's doing)

anonymous · Answer

Not Sure... hmmm i get back to u later

anonymous · Answer

Refer to the Mathematica Home Edition attachment.

anonymous · Answer

That doesn't prove anything.

anonymous · Answer

How about this one. http://users.rcn.com/mwhitney.massed/quadratic_formula_proof.html

anonymous · Answer

That's the ticket :).  It's the same method that I use to solve quadratic equations and it's so much better than sticking numbers into a formula.  Half the battle I have is trying to get my students out of bad habits like this.

anonymous · Answer

Isn't it true though that at Uni these days, math (particularly applied) is all about getting as many "procedures/methods" down the students as possible ie plug the numbers in, don't worry about the why of it.

anonymous · Answer

Absolutely, and unfortunately it's not just applied.  The entire education system (in England anyway) seems to be about teaching people to pass exams, not to actually understand the material with which they are presented.  Then the students don't seem to take any initiative, happy to just 'get by' with their passing grades.  It's such a shock for those who continue to a level where that attitude not tolerated, and will also cause them to fail.