If the difference between the corresponding roots of the equations `x^(2)+ax+b=0` and `x^(2)+bx+a=0(a1=b)` is the same, find the value of `a+b`.

Explanation

Let `alpha, beta` be the roots of `x^(2)+ax+b=0` and `gamma, delta` be the roots of `x^(2)+bx+a=0` then given
`alpha-beta=gamma-delta`
`=(sqrt(a^(2)-4b))/1=(sqrt(b^(2)-4a))/1 [ :' alpha-beta=(sqrt(D))/a]`
`impliesa^(2)-4b=b^(2)-4a`
`implies(a^(2)-b^(2))+4(a-b)=0implies(a-b)(a+b+4)=0`
`:'a-b!=0`
`:.a+b+4=0` or `a+b=-4`