Problem: If mmm and nnn are the roots of x2+mx+n=0,mβ 0,nβ 0x^{2}+m x+n=0, m \neq 0, n \neq 0x2+mx+n=0,mξ =0,nξ =0, then the sum of the roots is:
Answer Choices:
A. β12-\dfrac{1}{2}β21β
B. β1-1β1
C. 12\dfrac{1}{2}21β
D. 111
E. undeterminedundeterminedundetermined Solution:
m+n=βm\mathrm{m}+\mathrm{n}=-\mathrm{m}m+n=βm and mn=nβ΄m=1,n=β2β΄ m+n=β1\mathrm{mn}=\mathrm{n} \quad \therefore \mathrm{m}=1, \mathrm{n}=-2 \quad \therefore \mathrm{~m}+\mathrm{n}=-1mn=nβ΄m=1,n=β2β΄ m+n=β1.