Number of integral values of ‘b’ for which the origin and the point (1 , 1) lie on the same side of the straight line a2x+aby+1=0,  for  all  a∈R−{0}  is

Since (0 , 0) and (1 , 1) lie on the same side of line L=0, so  L11, L22  have same sign , hence L11·L22>0          ⇒    a2+ab+1>0     for all a∈R-0              ⇒ ∆ <0    since  a2 coefficient =1, quadratic expression in terms of 'a' have same sign         ⇒ b2-4 <0    ⇒  b ∈-2,2 ⇒b =-1,0,1