Problem:
The nonzero coefficients of a polynomial with real coefficients are all replaced by their mean to form a polynomial . Which of the following could be a graph of and over the interval ?
Answer Choices:
A. .jpg)
B. .jpg)
C. .jpg)
D. 
E. .jpg)
Solution:
The sum of the coefficients of and the sum of the coefficients of will be equal, so . The only answer choice with an intersection at is . (The polynomials in graph are and .)
The problems on this page are the property of the MAA's American Mathematics Competitions