Problem: Compute the sum of all the roots of (2x+3)(x−4)+(2x+3)(x−6)=0(2 x+3)(x-4)+(2 x+3)(x-6)=0(2x+3)(x−4)+(2x+3)(x−6)=0.
Answer Choices:
A. 7/27 / 27/2 B. 444 C. 555 D. 777 E. 131313 Solution:
Factor to get (2x+3)(2x−10)=0(2 x+3)(2 x-10)=0(2x+3)(2x−10)=0, so the two roots are −3/2-3 / 2−3/2 and 5 , which sum to 7/2\boxed{7 / 2}7/2​.
The problems on this page are the property of the MAA's American Mathematics Competitions