Problem:
For how many values of the constant will the polynomial have two distinct integer roots?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
In order for the given polynomial to have two distinct integer roots, the polynomial must factor as the product , where and are integers, with and . In each case, . The choices for and are then , , and , yielding , and -13 , respectively. Thus there are values for . (Note that the ordered pairs and produce the same value of , so the pairs and so forth can be ignored.)
The problems and solutions on this page are the property of the MAA's American Mathematics Competitions