# 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