Question

The no. of values of $x$ in the interval $[0,3\pi ]$ satisfying the equation $2{\sin }^{2}x+5\sin x-3=0$ is

• A. $1$
• B. $4$
• C. $6$
• D. $2$

Answer 1

The correct option is B $4$

The roots of the given equation $2{\sin }^{2}x+5\sin x-3=0$
are $\sin x=-3$ and $\sin x=\frac{1}{2}$
The first case is never possible.
And for the second case, $\sin x$ attains the value $\frac{1}{2}$ ,$4$ times in the interval [$0,3\pi$]
Hence, option 'B' is correct.