The smallest positive integral value of a for which the greater root of the equation x^2- (a^2+a+1 ) x+a (a^2+1 )=0 lies between the roots of the equation x^2-a^2 x-2 (a^2-2 )=0 , is less than:

Step-by-step solution

x^2-a x- (a^2+1 ) x+a (a^2+1 )=0 (x-a) (x- (a^2+1 ) )=0 Clearly greater root is a^2+1= (let). Let f(x)=x^2-a^2 x-2 (a^2-2 )=0 Then the condition that lies between the roots of f(x) is f( ) 5 from where we get least positive integral values of a as 3 . (a) 27 27 27 =27^ 1 / 2-1 / 4+1 / 8 =3 (b) 4 4 4 . =4^ 1 / 2+1 / 4+1 / 8+ =4 (c) 5 5 5 5 = 5 ^ 1+1 / 2+1 / 4+ . =5 (d) 2+ 2+ 2+ =2