2011 AIME II Problems/Problem 8
Revision as of 19:26, 31 March 2011 by NewAlbionAcademy (talk | contribs)
Problem:
Let ,
,
,
,
be the 12 zeroes of the polynomial
. For each
, let
be one of
or
. Then the maximum possible value of the real part of
can be written as
, where
and
are positive integers. Find
.
Solution: Let me first note that this is a hastily compiled solution.
<geogebra>973797c41824115b678d18138dff008b8acfda12</geogebra>
If you multiply one of those dots on the circle(of radius 8) by i, you move it 90 degrees clockwise. You want everything to be as far right as possible, and when you are done, you find that you get 784 when you add everything.