If the equations x2−ax+b=0 and x2+bx−a=0 have a common root, then

Let λ be the common root of the given equations Then,λ2−aλ+b=0 and λ2+bλ−a=0On subtracting, we getλ(a+b)−(a+b)=0⇒a+b=0 or, λ=1Putting λ=1 in λ2−aλ+b=0, we get 1−a+b=0⇒a−b=1