1997 AIME Problems/Problem 14
Problem
Let and
be distinct, randomly chosen roots of the equation
. Let
be the probability that
, where
and
are relatively prime positive integers. Find
.
Solution
The solution requires the use of Euler's formula:
If , where k is any constant, the equation reduces to:
Now, substitute this into the equation:
Now, let be the root corresponding to
, and let
be the root corresponding to
. The magnitude of
is therefore: