Problem:
Let a,b, and c be three distinct one-digit numbers. What is the maximum value of the sum of the roots of the equation (xβa)(xβb)+(xβb)(xβc)=0 ?
Answer Choices:
A. 15
B. 15.5
C. 16
D. 16.5
E. 17
Solution:
If (xβa)(xβb)+(xβb)(xβc)=0, then (xβb)(2xβ(a+c))=0, so the two roots are b and 2a+cβ. The maximum value of their sum is 9+28+7β=16.5β.
The problems on this page are the property of the MAA's American Mathematics Competitions