Problem: If mmm and nnn are the roots of x2+mx+n=0,m≠0,n≠0x^{2}+m x+n=0, m \neq 0, n \neq 0x2+mx+n=0,mî€ =0,nî€ =0, then the sum of the roots is:
Answer Choices:
A. −12-\dfrac{1}{2}−21​
B. −1-1−1
C. 12\dfrac{1}{2}21​
D. 111
E. undeterminedundeterminedundetermined Solution:
m+n=−m\mathrm{m}+\mathrm{n}=-\mathrm{m}m+n=−m and mn=n∴m=1,n=−2∴ m+n=−1\mathrm{mn}=\mathrm{n} \quad \therefore \mathrm{m}=1, \mathrm{n}=-2 \quad \therefore \mathrm{~m}+\mathrm{n}=-1mn=n∴m=1,n=−2∴ m+n=−1.