AIME II #9 2003

[stupidityismygam]

Consider the polynomials [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] Given that [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] are the roots of [unparseable or potentially dangerous latex formula] find [unparseable or potentially dangerous latex formula]

[zefuri]

I didnt like this one it was lame.

[stupidityismygam]

NEWTON SUMS :), everybody loves newton sums...

[zefuri]

OH WAIT THIS WAS BEFORE I LEARNED NEWTON SUMS =OOOOO I NEED TO OWN

[Michael T]

Btw, thanks to stephen for helping a little bit.


ModNinjaEdit: The nth newton sum of a polynomial of degreee p is defined as
[unparseable or potentially dangerous latex formula] where [unparseable or potentially dangerous latex formula] is a zero of the polynomial
\ModNinjaEdit


Using newton sums for Q(x), we get:

[unparseable or potentially dangerous latex formula]

After which we do some neato algebra I stuff and get:

[unparseable or potentially dangerous latex formula]


ModNinjaEdit: by the definition of Newton Sums, [unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
\ModNinjaEdit


Apparently substituting [unparseable or potentially dangerous latex formula] for [unparseable or potentially dangerous latex formula] in [unparseable or potentially dangerous latex formula] gets you the right answer. So, we do this:

[unparseable or potentially dangerous latex formula]
Which equals 6.
[unparseable or potentially dangerous latex formula]

[Michael T]

Thank you to stephen for modninja'ing my post and explaining.