Search any question & find its solution
Question:
Answered & Verified by Expert
The number of values of $x$ in $[0,2 \pi]$ satisfying the equation $3 \cos 2 x-10 \cos x+7=0$ is
Options:
Solution:
2631 Upvotes
Verified Answer
The correct answer is:
4
Given, $3 \cos 2 x-10 \cos x+7=0$
$$
\begin{aligned}
&\Rightarrow \quad 6 \cos ^{2} x-10 \cos x+4=0 \\
&\Rightarrow 2(3 \cos x-2)(\cos x-1)=0 \\
&\Rightarrow \quad\left[\cos 2 x=2 \cos ^{2} x-1\right]
\end{aligned}
$$
Hence, $\cos x$ is positive in Ist and IVth quadrants. Hence, the total number of solutions is 4 .
$$
\begin{aligned}
&\Rightarrow \quad 6 \cos ^{2} x-10 \cos x+4=0 \\
&\Rightarrow 2(3 \cos x-2)(\cos x-1)=0 \\
&\Rightarrow \quad\left[\cos 2 x=2 \cos ^{2} x-1\right]
\end{aligned}
$$
Hence, $\cos x$ is positive in Ist and IVth quadrants. Hence, the total number of solutions is 4 .
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.