Question

The quadratic equation \(8\sec^2x-6\sec x+1=0\) has

• A. No real roots
• B. Two real roots
• C. Many roots
• D. Only one real root

Hint:

Convert trigonometric quadratic to algebraic variable.

Answer 1

The Correct Option is B

Step 1: Let \(y=\sec x\).
Step 2: Equation becomes: \[ 8y^2-6y+1=0. \] 
Step 3: Discriminant: \[ \Delta=36-32=4>0. \] 
Step 4: Two real \(y\) → two real \(x\). Hence → (B).