2014 USAMO Problems/Problem 1
Contents
[hide]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
Using the hint we turn the equation into .
Solution
The value in question is equal to
where
. Equality holds if
, so this bound is sharp.