Math Is Fun Forum

Hi,

How can I derived the conic section discriminant from the general equation Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0

The book I'm reading says that it's taken from A,B,C. I don't see how Ax^2 + Bxy + Cy^2 can be turned into b^2-4ac. I know that Ax^2 + Bx + C can be used to get the discriminant from learning about quadratics, but like I said the book says it uses A,B,C. My best guess is that they meant it's derived from Ax^2 + Dx + F. I'm not sure but I think I'm interpreting the text wrong. Can someone please clear this up for me? Thanks.

I saw this problem on sosmath.com - http://www.sosmath.com/algebra/pfrac/pfrac.html

x^3 - 4x^2 + 5

and it's suppose to factor out to (x+1)(x^2-5x+5) and I've been sitting here trying to get it to that form but I only end up with (x^2+5)(x-4). Can someone please shed some light to how this can be factored out to (x+1)(x^2-5x+5). Thanks!

So, I've survived all my math classes from elementary school through college (BS), but I've gotten through without understanding why I'm learning what I was being taught. I felt lost and still feel lost. I'm finding it difficult seeing the whole picture. I'm looking for a chart, map or list of some kind that shows the major areas of math and how they are related to each other. I think if I have something visual to look at I will have a better sense of how everything fits together. Also, it would be helpful if it described where that area of mathematics is applied. Do you know where I can find this? Or can you help me out and make one. Thanks! John