Suppose $f(x)$ is a twice differentiable function on $[a,b]$ such that $$f(a)=0=f(b)$$ and $$x^2\frac{d^{2}f(x)}{d{x}^2}+4x\frac{df(x)}{dx}+2f(x)>0\text{ for all }x\in (a,b)\text{ . }$$ Then,$$ (a) $f$ is negative for all $x\in (a,b).$ $$ (b) $f$ is positive for all $x\in (a,b).$ $$ (c) $f(x)=0$ for exactly one $x\in (a,b).$ $$ (d) $f(x)=0$ for atleast two $x\in (a,b).$