Difference between revisions of "Mock AIME 3 2006-2007 Problems/Problem 3"
(Created page with " == Problem == Let <math>P(x) = 2x^{59} - x^2 - x - 6</math>. If <math>Q(x)</math> is a polynomial whose roots are the 59th powers of the roots of <math>P(x)</math>, then find t...") |
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Revision as of 20:52, 15 February 2015
Problem
Let . If is a polynomial whose roots are the 59th powers of the roots of , then find the sum of the roots of .
Solution
Let denote the roots of P. Then, . Therefore, .
Denote. So . To find , use Newton's recursive sums:
.
Solving, we get .