Question

Find the number of values of $x$ in $[0,5\pi ]$ satisfying the equation $3{\cos }^{2}x-10\cos x+7=0$.

Answer 1

$3{\cos }^{2}x-10\cos x+7=0$

$3co{s}^{2}x-7\cos x-3\cos x+7=0$

$\Rightarrow 3\cos x(\cos x-1)-7(\cos x-1)=0$

$\Rightarrow (\cos x-1)(3\cos x-7)=0$

$\Rightarrow \cos x=1,\cos x=\frac{7}{3}$

$\downarrow$

Not possible

$\because \cos xϵ[-1,1]$

So, $cosx=1$

(Refer to Image)

In $[0,\pi ]$ $\cos x=1$ at $1$ point.

So, $[0,5\pi ]$ $\cos x=1$ at $3$ point.