2010 AMC 10A Problems/Problem 21
Problem
The polynomial has three positive integer zeros. What is the smallest possible value of
?
Solution
By Vieta's Formulas, we know that is the sum of the three roots of the polynomial
.
Also, 2010 factors into
. But, since there are only three roots to the polynomial, two of the four prime factors must be multiplied so that we are left with three roots. To minimize
,
and
should be multiplied, which means
will be
and the answer is
.