1991 AIME Problems/Problem 7
Problem
Find , where
is the sum of the absolute values of all roots of the following equation:

Solution
Let . Then
, from which we hypothesize that
. The given finite expansion can then be easily seen to reduce to the quadratic equation
. The solutions are
. Therefore,
. We conclude that
.
See also
1991 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |