2001 AMC 12 Problems/Problem 19
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 ?
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 .