Sam1 wrote:

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.

Hence

0=m^2+am+b

0=n^2+an+b

1-2

gives

0=n^2-m^2 +a (n-m)

taking n-m common

(n-m) (n+m+a)=0

hence (n-m)=0 or (n+m+a)=0

n=m; (n+m)=-a

looking at statement a

a^2-4=4b

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.

NOW,

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 = 2

however,using option 2, we can not find out n-m.

Hence, A. Hope this helps.

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