Question

The equation \( (\cos p - 1)x^2 + (\cos p)x + \sin p = 0 \), where \( x \) is a variable with real roots. Then the interval of \( p \) may be any one of the following:

• A. \( (0, 2\pi) \)
• B. \( (-\pi, 0) \)
• C. \( (-\frac{\pi}{2}, \frac{\pi}{2}) \)
• D. \( (0, \pi) \)

Hint:

For a quadratic equation to have real roots, the discriminant (i.e., \( b^2 - 4ac \)) must be non-negative.