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. $(0,\pi )$

Answer 1

Answer: (D)

$(0,\pi )$

for real roots , discriminant is greater than or equal to zero
that is ${\cos }^{2}p-4\sin p(\cos p-1)\ge 0$
now $\cos p-1\le 0$
so if $\sin p\ge 0$ then our task is done
now $\sin p\ge 0$ holds in first and second quadrants.