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JEE Main 1990 Mathematics question on Complex Numbers and Quadratic Equations

The equation (cos⁡p−1)x2+(cos⁡p)x+sin⁡p=0(\cos p - 1)x^2 + (\cos p)x + \sin p = 0 in the variable xx, has real roots. Then, pp can take any value in the interval
  1. A.
    (0,2π)(0, 2\pi)
  2. B.
    (−π,0)(-\pi, 0)
  3. C.
    (−π2,π2)\left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right)
  4. D.
    (0,π)(0, \pi)
Show answer

Correct option: D

[1990]

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