Problem:
Suppose that a and b are nonzero real numbers, and that the equation x2+ax+b=0 has solutions a and b. Then the pair (a,b) is
Answer Choices:
A. (−2,1)
B. (−1,2)
C. (1,−2)
D. (2,−1)
E. (4,4)
Solution:
The given conditions imply that
x2+ax+b=(x−a)(x−b)=x2−(a+b)x+ab
so
a+b=−a and ab=b.
Since bî€ =0, the second equation implies that a=1. The first equation gives b=−2, so (a,b)=(1,−2)​.
The problems on this page are the property of the MAA's American Mathematics Competitions