f(x) is an even function, x = 1 is a point of minima and x = 2 is a point of maxima for y = f(x). Further lim(x ∞) f(x) = 0, and lim(x 0) f(x) = ∞. f(x) is increasing in (1, 2) & decreasing everywhere in (0, 1) ∪ (2, ∞). Also f(1) f(1) = 3 & f(2) = 5. Then
(A) f(x) = 0 has no real roots
(B) y = f(x) and y = If(x)| are identical functions
(C) f''(x) =0 has exactly four real roots whose sum is zero
(D) f''(x) = 0 has exactly four real roots whose sum is 6
