a possible positive value of ' a ', for which f^ ' (x)=0 has equal roots, is

Step-by-step solution

Given, f(x)= ₀^x [(a+1)(t+1)^2-(a-1) (t^2+t+1 ) ] d t Now, f^ (x)=(a+1)(x+1)^2-(a-1) (x^2+x+1 )=0 2 x^2+(3+a) x+2 a=0 for equal roots, (3+a)^2-4 4 a=0 a=1