The number of values of x in the interval \[\left[ {0,3\pi } \right]\,\] satisfying the equation \[2{\sin ^2}x + 5\sin x - 3 = 0\] is
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Official solution
\[2{\sin ^2}x + 5\sin x - 3 = 0\]
\[ \Rightarrow \left( {\sin x + 3} \right)\left( {2\sin x - 1} \right) = 0\]
\[\sin x = {1 \over 2}\] and \[\,\,\sin x \ne - 3\]
Given that \[x \in \left[ {0,3\pi } \right]\]
So possible values of x are \[30^\circ \], \[150^\circ \], \[390^\circ \], \[510^\circ \]. That means x have 4 values.