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 a=1,b=2,c=3,d=4⇒ given equation becomes  (x−1)(x−3)+2(x−2)(x−4)=0⇒ 3x2−16x+19=0 Now D=(−16)2−4.3.19 =256−228 =28>0Hence roots are real and distinct.