Suppose f(x) is a polynomial of degree four having critical points at -1,0,1 .If T={x∈R:f(x)=f(0)} then the sum of squares of all the elements of T is

Given f(x) is a polynomial of degree 4 and having critical points at -1,0,1Hence, f1(x) = λx (x2−1) = λ(x3−x) (λ≠0)Integrate f(x) = λ x44−x22 + k= λx44−x22 +f(0) If f(x)=f(0)⇒λx44-x22=0⇒x2=0 or x2=2⇒x=0,x=±2 Sum of the squares of the values of x in T is 0 + 2 + 2 = 4.