This is how I am solving it. Will appreciate your help to tell me where I am going wrong.
since m and n are the two points through which the graph passes they will both satisfy the equation.
0=n^2-m^2 +a (n-m)
taking n-m common
hence (n-m)=0 or (n+m+a)=0
looking at statement a
a will be something in terms of b but we will not the exact value of a.
Please tell me where am I making a mistake
Hi Sam1,Basically we need to find the value of n-m, the difference between the roots.
What you have done is, showed the sum of the roots , n+m = - a ---(1)
which you have deduced right.
multiplying the above equation by n yields:
n^2+m*n = -a*n
or n^2 +m*n + a*n =0
or m*n - b = 0 ---- (as n^2+a*n+b =0 ,n being one of the roots)
or m*n = b ----------(2)
Now, (n-m)^2 = n^2 -2*m*n + m^2
= (n+m)^2 - 4*m*n
using eqn(1) and eqn(2), we have
(n-m)^2 = a^2 - 4*b
or (n-m) = sq.root(a^2 - 4*b)
Now from answer choices,using option 1,we can find n-m
however,using option 2, we can not find out n-m.
Hence, A. Hope this helps.Press kudos if you wish to appreciate