University of South Carolina High School Math Contest/1993 Exam/Problem 12
Problem
If the equations and
have exactly one root in common, and
then the other root of equation
is
![$\mathrm{(A) \ }\frac{c-a}{b-d}d \qquad \mathrm{(B) \ }\frac{a+c}{b+d}d \qquad \mathrm{(C) \ }\frac{b+c}{a+d}c \qquad \mathrm{(D) \ }\frac{a-c}{b-d} \qquad \mathrm{(E) \ }\frac{a+c}{b-d}c$](http://latex.artofproblemsolving.com/3/0/e/30e4811f03eb46eb9bea68efe4334a588bd1a071.png)
Solution
Let have roots
and
have roots
. Thus:
Thus, we know that and our answer choice must equal
. The answer is
.