Question

The number of values of $x$ satisfying the equation $3{\sin }^{2}x-7\sin x+2=0$ in the intarval $[0,5\pi ]$.

• A. $0$
• B. $5$
• C. $6$
• D. $10$

Answer 1

Answer: (C)

$6$

Given quadratic equation is $3{\sin }^{2}x-7\sin x+2=0$

$\Rightarrow \sin x=\frac{7\pm \sqrt{49-24}}{6}=\frac{7\pm 5}{6}=\frac{1}{3},2$

Since $\sin x<1$ , the possible value of $\sin x$ is $\frac{1}{3}$

In the interval $[0,\pi ]$ , the number of solutions is $2$.

In the interval $[\pi ,2\pi ]$ , the number of solutions is $0$.

Therefore in interval $[0,5\pi ]$ , the number of solutions is $2+0+2+0+2=6$

Therefore option $C$ is correct.