1984 USAMO Problems/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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See Also

1984 USAMO (Problems • Resources)
Preceded by First Problem	Followed by Problem 2
1 • 2 • 3 • 4 • 5
All USAMO Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.