Consider the equation x2−2x+mx2−2x+n=0 (where m and n are real numbers). Let the roots α,β,γ,δ(α<β<γ<δ )of the equation form an A.P. with first term equal  to 14 . Then the value of mn is

Given first term being A=14 So, 4 roots in A.P. are 14,14+d,14+2d,14+3d Now given, x2−2x+mx2−2x+n=0We can see that the sum of the roots in both the factors is 2. Hence, 14+14+d+14+2d+14+3d=4∴ d=12 Hence, roots are 14,34,54 and 74 .  Here, 34+54=2 and 14+74=2 Hence, n=34×54=1516 and  m=14×74=716