Suppose $f ( x )$ is a twice differentiable function on $[ a , b ]$ such that
$$f ( a ) = 0 = f ( b )$$
and
$$x ^ { 2 } \frac { d ^ { 2 } f ( x ) } { d x ^ { 2 } } + 4 x \frac { d f ( x ) } { d x } + 2 f ( x ) > 0 \text { for all } x \in ( a , b )$$
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 at least two $x \in ( a , b )$.