Ans: B
$\begin{array}{rcl}
5 \sin^2 \theta + \sin \theta – 4 & = & 0 \\
(5 \sin \theta -4)(\sin \theta +1) & = & 0 \\
\end{array}$
$\begin{array}{rcl}
5 \sin^2 \theta + \sin \theta – 4 & = & 0 \\
(5 \sin \theta -4)(\sin \theta +1) & = & 0 \\
\end{array}$
Therefore, $\sin \theta = \dfrac{4}{5}$ or $\sin \theta =-1$.
Consider $\sin \theta = \dfrac{4}{5}$, $\theta = 53.1^\circ$ or $\theta = 127^\circ$.
Consider $\sin \theta = -1$, $\theta = 270^\circ$.
Therefore, there are $3$ roots.
