Tuesday, 28 December 2010

Just because I can...

So now I have $\LaTeX{}$ fully up and running and function able, I thought I would start by saying why I have decided to actually bother getting it working. Being a mathematics student in my final year, I have to complete a 'final year project' (Dissertation or Thesis to anyone else), and as with most scientific papers, the form they are presented in is indeed $\LaTeX{}$. My final year project is going to be based upon statistical forecasting, and the software that is used within (but you shall hear more about this in another post).
For now I'm going to spend the rest of this post with a nice bit of proof showing how we get the quadratic equation from.

If you look online there are many long winded ways of showing proof for this formula. Most take up a page and can be quite hard to follow: I prefer this method.
Like with most quadratic formulas, we start with the basic idea that \[ax^{2}+bx+c=0\] From here, we can start by multiplying through by $4a$ (You just do, ok?), which would give us something like this: \[4a^{2}x^{2}+4abx+4ac\]With a little magic, which I like to call completing the square, we can now tidy up $4a^{2}x^{2}+4abx$ to make a much nicer \[\left(2ax+b \right)^{2}-b^{2}\]
So now we have an equation that looks a little something like this: \[\left(2ax+b \right)^{2}-b^{2}+4ac=0\]
Taking $-b^{2}+4ac$ over to the other side, then square rooting leaves us with:\[2ax+b=\pm\left(b^{2}-4ac\right)\] Now all that is left to do is minus the $b$ and divide through by the $2a$, leaving us with the oh so lovely: \[x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\]


Anonymous said...

I thoroughly enjoyed your post and look forward to reading more of your work in the coming months.

ps. love the new background :P

Cameron Wyatt said...

Looks pretty interesting man. Best of luck with everything at your university.