Problem:
The sum of the zeros, the product of the zeros, and the sum of the coefficients of the function are equal. Their common value must also be which of the following?
Answer Choices:
A. $the coefficient of $
B. $the coefficient of $
C. $the -intercept of the graph of $
D. $one of the -intercepts of the graph of $
E. $the mean of the -intercepts of the graph of $
Solution:
The product of the zeros of is , and the sum of the zeros is . Because these two numbers are equal, , and the sum of the coefficients is , which is the coefficient of . To see that none of the other choices is correct, let . The zeros of are , so the sum of the zeros, the product of the zeros, and the sum of the coefficients are all -2 . However, the coefficient of is -4 , the -intercept is 4 , the -intercepts are , and the mean of the -intercepts is -1 .
The problems on this page are the property of the MAA's American Mathematics Competitions