Question

The equation (cos p - 1)$x^2$ + (cos p)x + sin p = 0 in variable x has real roots, if p belongs to the interval

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

(cos p - 1)$x^2$ + (cos p)x + sin p = 0 .....(1)

Discriminant of (1) is given by D = $co{s}^2$ p - 4 (cos p - 1)sin p = $co{s}^2$ p + 4 (1 - cos p) sin p

Note that $co{s}^{2}p\ge 0,1-cosp\ge 0.Thus,D\ge 0ifsinp\ge 0i.eifpϵ(0,\pi )$