Difference between the corresponding roots of x 2 + a x + b = 0 & x 2 + b x + a = 0 is same and a ≠ b , ⁡ then

Step-by-step solution

Let α ,   β   &   γ ,   δ are the roots of the equations x 2 + a x + b = 0 and x 2 + b x + a = 0 respectively. Therefore, α + β = - a α β = b Also, for the second equation γ + δ = - b γ δ   =   a Given that, α - β = γ - δ ⇒ α - β 2 = γ - δ 2 ⇒ α + β 2 - 4 α β = γ + δ 2 - 4 γ δ ⇒ a 2 - 4 b = b 2 - 4 a ⇒ a 2 - b 2 + 4 a -