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

• A

  $0$
• B

  $5$
• Correct answer
  C

  $6$
• D

  $10$

Solution

$3{\sin }^{2}x-7\sin x+2=0$
$3{\sin }^{2}x-6\sin x-\sin x+2=0$
$\left(3\sin x-1\right)\left(\sin x-2\right)=0$
$\Rightarrow \sin x=\frac{1}{3},\sin x=2$ not possible

Fro the figure, $6$ roots in $\left[0,5\pi \right]$

Hence, the correct answer is option: 'C'.