2003 AIME II Problems/Problem 15

Problem

Let

$P(x) = 24x^{24} + \sum_{j = 1}^{23}(24 - j)(x^{24 - j} + x^{24 + j}).$

Let $z_{1},z_{2},\ldots,z_{r}$ be the distinct zeros of $P(x),$ and let $z_{k}^{2} = a_{k} + b_{k}i$ for $k = 1,2,\ldots,r,$ where $i = \sqrt { - 1},$ and $a_{k}$ and $b_{k}$ are real numbers. Let

$\sum_{k = 1}^{r}|b_{k}| = m + n\sqrt {p},$

where $m,$ $n,$ and $p$ are integers and $p$ is not divisible by the square of any prime. Find $m + n + p.$

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

2003 AIME II (Problems • Answer Key • Resources)
Preceded by Problem 14	Followed by Last Question
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
All AIME Problems and Solutions

Page

Toolbox

Search

2003 AIME II Problems/Problem 15

Problem

Solution

See also