Let $f(x)$ be a 3rd degree polynomial such that $f(x^2)=0$ has exactly $4$ distinct real roots, if f(k) =0, $k \neq \alpha^2, \beta^2$ ( where $\pm \alpha, \pm \beta)$ are roots of equation $f(x^2)=0,$ then ( which of the following is correct)
(a) $k <0$
(b) $k >0$
(c) k $\leq 0$
(d) $k \geq 0$
Please suggest how to get this relation of k w.r.t the given polynomial. I am having no clue how to proceed to get the options... will be greatful to you... thanks....