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 |