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