I recently placed a question based on quadratics and received a few valuable answers. One of them was a comment in an answer with a link in it which I found useful. But unfortunately the webpage (of which the link was sent) was in Russian (which is totally a foreign language to me) and so I could not understand even a word of it! Thus my request to you all is
"Can anyone please provide a link to the webpage in English or suggest weblinks to similar pages in English (I mean with explanations on quadratics,in particular that can help solve my question) "
I would be highly obliged to you for this.Thanks.
http://tutorial.math.lamar.edu/Classes/Alg/Solving.aspx. Try this. It's a comprehensive website that explains a lot of maths. The link is the algebra page which deals with polynomials and such. You'll find the quadratic equations section in the list. Hope that helps
I'm sorry I didn't read your question properly. Your proof is entirely correct, but it assumes that every quadratic actually has a real solution. The equation $a+b = -m$ is only true if $(x-a)(x-b)$. m is a real number, but the factor expression is true for both real and complex numbers. So the problem arises when a and b are complex roots. The quick solution is to create a bound on a and b such that they are not complex numbers hint the discriminant ($m^2 - 4\cdot1\cdot6$) cannot be a negative. I'd suggest learning about complex numbers in general so that you don't run into these problems as much, since they are a fundamental part of mathematics. (And are interesting).
http://nrich.maths.org/1403