\begin{aligned}
&\text { Let } f:[a, b] \rightarrow \mathbb{R} \text { be differentiable on }[a, b] \& k \in \mathbb{R} . \text { Let } f(a)=0=f(b) \\
&\text { Also let } J(x)=f^{\prime}(x)+k f(x) . \text { Then } \\
&\begin{array}{ll}
\text { (A) } J(x)>0 \text { for all } x \in[a, b] & \text { (B) } J(x)<0 \text { for all } x \in[a, b] \\
\text { (C) } J(x)=0 \text { has at least one root in }(a, b) & \text { (D) } J(x)=0 \text { through }(a, b)
\end{array} \\
&\text { }()
\end{aligned}