Let α1 and α2 be roots of the equation x2+ax+b=0 Therefore, α1+α2=−a and α1α2=b and β1 and β2 be the roots of the equation x2+bx+a=0 Therefore, β1+β2=−b and β1,β2=a Given that α1−α2=β1−β2 ⇒(α1+α2)2−4α1α2=(β1+β2)2−4β1β2 ⇒(−a)2−4b=b2−4a ⇒a2−b2+4a−4b=0 ⇒(a−b)(a+b)+4(a−b)=0 ⇒(a−b)(a+b+4)=0 Therefore, a−b=0 and a+b+4=0