Question

The number of solutions to the equation $12{\cos }^{3}x-7{\cos }^{2}x+4\cos x=9$ is

• A. 0
• B. 2
• C. Infinite
• D. None of these

Answer 1

Answer: (C)

The given equation is $(\cos x-1)\left(12{\cos }^{2}x+5\cos x+9\right)=0$
$\Rightarrow \cos x=1$ only as the other factor gives imaginary roots
$\Rightarrow \cos x=1\Rightarrow x=2n\pi$
Hence, it has infinite solutions as $n\in Z$.