Question

The number of values of x in the interval $[0,3\pi ]$ satisfying the equation $2{\sin }^{2}x+5\sin x-3=0$ is?

• A. $6$
• B. $1$
• C. $2$
• D. $4$

Answer 1

Answer: (D)

$4$

$(\sin x+3)(2\sin x-1)=0$

$\therefore \sin x=\frac{1}{2}$ as $\sin x\ne -3$

$\therefore x-\frac{\pi }{6},\pi -\frac{\pi }{6}=\frac{5\pi }{6}$ i.e., two values in $0$ to $\pi$.

No value in $\pi$ to $2\pi$ as $\sin \theta$ will be $-$ive and two values again in $2\pi$ to $3\pi$. Thus there will be only four values of x.