Difference between revisions of "2014 USAMO Problems/Problem 1"
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Factor <math>x^2 + 1</math> as the product of two linear binomials. | Factor <math>x^2 + 1</math> as the product of two linear binomials. | ||
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==Solution== | ==Solution== |
Revision as of 19:04, 14 May 2014
Problem
Let be real numbers such that and all zeros and of the polynomial are real. Find the smallest value the product can take.
Hint
Factor as the product of two linear binomials.
Solution
The value in question is equal to where . Equality holds if , so this bound is sharp.