Problem:
What is the sum of all possible values of for which the polynomials and have a root in common?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Factoring as shows that its roots are 1 and 2 . If 1 is a root of , then and . If 2 is a root of , then and . The sum of all possible values of is .
The problems on this page are the property of the MAA's American Mathematics Competitions