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:

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Substituting given values obtains the following:

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Multiplying the * equation by 16 gives

. Adding it to the previous equation gives

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