Let `f(x)` be a differentiable function with `f(1)f(-1)!=0.` Define a function `g(x)=(x^2-1)/(f(x))` . If `g(x)` does not follow Rolles theorem in `[-1,1],` then which of the following options is/are FALSE? `(a)``f(x)=0` cannot have any root in `[-1,1]``.` `(b)` `f(x)=0` has at least one root in `[-1,1]``.` `(c)` `f(x)` is zero at at least one point in `[-1,1]``.` `(d)` `f(x)` cannot satisfy Rolles theorem in `[-1,1]``.`