Question

The number of values of $x$ in $[0,5\pi ]$ satisfying the equation $3\cos 2x-10\cos x+7=0$ is

• A. $5$
• B. $6$
• C. $8$
• D. $10$

Answer 1

The correct option is C $8$

$3cos2x-10cosx+7=0$
$3(2co{s}^{2}x-1)-10cosx+7=0$
$3co{s}^{2}x-5cosx+2=0$
$(3cosx-2)(cosx-1)=0$
$cosx=2/3$ or $cosx=1$
therefore general solution is,
$x=2n\pi \pm co{s}^{-1}\left(2/3\right)$ or $x=2n\pi$
so the solution in given interval is,
$x=0,co{s}^{-1}\left(2/3\right),2\pi -co{s}^{-1}\left(2/3\right),2\pi ,2\pi +co{s}^{-1}\left(2/3\right),4\pi -co{s}^{-1}\left(2/3\right),4\pi ,4\pi +co{s}^{-1}\left(2/3\right)$
Hence, option 'C' is correct.