what do you know about quadratic equations?

RolandIRL

me and two others have to do a mini-project about quadratic equations - what they are, how did mathematicians centuries ago solve them, etc - for about 10-15 minutes in a workshop.
is there any other ways to solve them besides the -b formula, completing the square and letting alpha and beta equal the roots?

any help would be much appreciated.
thanks

LeixlipRed

There are loads of old methods for solving certain types of quadratics. Check this out, some historical stuff there.

LeixlipRed

Actually, I'm thinking of methods of solving cubics, which are the interesting ones. Tartaglia and that. The Babylonians were the first to play around with quadratics, have a google, that link I supplied is more relevant for cubics.

Fremen

Look up the pythagorean brotherhood, too.
They solved x^2 = 2 and got a nasty shock.

It depends how deep you want to go.... the Princeton companion to mathematics has some *deep* stuff on algebraic geometry and arithmetic geometry, but you probably need to be in second year of a maths degree to follow it.

Edit:
Going into some detail on the Newton-raphson method might be good. You could do some stuff on Newton fractals if you know about complex numbers. would make for some interesting pictures in your presentation.

LeixlipRed

Yeh, the Newton-Rapshon method is a good idea actually. It's simple enough to explain and derive too.

RolandIRL

thanks for the replys. i'm only in first year science, not a dedicated maths degree course. don't need to go into too much depth. forgot about the whole newton-raphson method.

Fremen

Definitely have a crack at newton fractals then. They're easy and they'll liven up what could otherwise be a slightly dull topic.

RolandIRL

the pictures on wikipedia look so much like kaleidascopes.
i'm going to have another look at my 2nd level maths book again.
could you also use de moivre's theorem to solve quad. equations with complex roots? i think i remember doing that in 5th year of secondary school.