2001 AMC 12 Problems/Problem 19
Problem
The polynomial has the property that the average of its zeros, the product of its zeros, and the sum of its coefficients are all equal. The
-intercept of the graph of
is 2. What is
?
Solution
We are given . So the product of the roots is
by Vieta's theorem. Vieta's also tells us
is the average of the zeros, so
. We are also given that the sum of the coefficients is -2, so
. So the answer is
.