2019 Mock AMC 10B Problems/Problem 7
Revision as of 14:41, 5 November 2023 by Excruciating (talk | contribs) (Created page with "Solution by excruciating: Subtracting <math>n</math> from both sides gives <cmath>x^2-8x+(96-n^2)=0.</cmath> For any quadratic <math>ax^2+bx+c</math>, the sum of the roots is...")
Solution by excruciating:
Subtracting 
from both sides gives ![\[x^2-8x+(96-n^2)=0.\]](http://latex.artofproblemsolving.com/4/7/6/476c486ab8d78e14586a70ad52981a61df5de091.png)
For any quadratic 
, the sum of the roots is 
So, the sum of the roots is 
. Note that whatever is does not affect the sum of the roots.
