If a, b, c,d  are four consecutive terms of an increasing A.P., then the roots of the equation (x−a)(x−c)+2(x−b)(x−d)=0, are

Let λ be the common difference of the increasing A.P. Then,     b=a+λ,c=a+2λ and d=a+3λ, where λ>0.∴ (x−a)(x−c)+2(x−b)(x−d)=0⇒ 3x2−2(3a+5λ)x+a(a+2λ)+2(a+λ)(a+3λ)=0Let D be its discriminant. Then,           D=4(3a+5λ)2−12a(a+2λ)−24(a+λ)(a+3λ)⇒ D=28λ2>0.Hence, the roots of the given equation are real and distinct.