Let α,β and γ,δ be the roots of the equations x2+ax+b=0 and x2+bx+a=0 respectively. ∴α+β=−a,αβ=b and γ+δ=−b,γδ=a Given |α−β|=|γ−δ| ⇒(α−β)2=(γ−δ)2 ⇒(α+β)2−4αβ=(γ+δ)2−4γδ ⇒a2−4b=b2−4a ⇒(a2−b2)+4(a−b)=0 ⇒a+b+4=0 ( as a≠b)