If (cosec^2θ – 4)x^2 + (cotθ + √3)x + cos^2 3π/2 = 0 holds true for all real x, then the most general values of θ can be given by (n ∈ Z) ​

Question

If (cosec²θ – 4)x² + (cotθ + √3)x + cos²\(\frac{3\pi}2\) = 0 holds true for all real x, then the most general values of θ can be given by (n ∈ Z)

a. \(2n\pi + \frac{11\pi}6\)

b. \(2n\pi + \frac{5\pi}6\)

c. \(2n\pi \pm \frac{7\pi}6\)

d. \(n\pi \pm \frac{11\pi}6\)

Answer 1

Correct option is a. \(2n\pi + \frac{11\pi}6\) & b. \(2n\pi + \frac{5\pi}6\)