Question

The number of roots of the quadratic equation $8{\sec }^2\theta -6\sec \theta +1=0$ is:

• A. Infinite
• B. $1$
• C. $2$
• D. $0$

Answer 1

The correct option is D $0$

$8{\sec }^2\theta -4\sec \theta -2\sec \theta +1=0$

$\Rightarrow (4\sec \theta -1)(2\sec \theta -1)=0$

$\Rightarrow \sec \theta =\frac{1}{4}$ or $\sec \theta =\frac{1}{2}$

$\Rightarrow \cos \theta =4$ or $\cos \theta =2$

Which is not possible

$\Rightarrow$number of roots of given equation is 0