1984 USAMO Problems/Problem 1
1984 USAMO Problem #1
Problem:
In the polynomial , the product of
of its roots is
. Find
.
Solution:
Let the four roots be . By Vieta's Formulas, we have the following:
*
Substituting given values obtains the following:
- Multiplying the equation by 16 gives
. Adding it to the previous equation gives