If are positive and are in AP, then the roots of the quadratic equation are complex for
Explanation for the correct option
Step 1: Determination of the value of
Step 2: Formation of the equation to find the required roots
The quadratic equation of the form then the real roots will be when the discriminant is greater than or equal to zero.
, where
Put the value in the above equation
Divide by on both the sides, then
Now, put the above equation will become,
Step 3: Solve the inequality by the perfect square method.
Add and subtract from the LHS,
Take the square root on both the sides,
Hence, option (A) is correct.