# The equation where X is a variable has real roots then the interval of P maybe any one of the following

Soumendu Majumdar
159 Points
4 years ago
Dear Student,
since the given equation has real roots, so the discriminant is always greater than or equal to zero.
so
$cos^2p\geq 4cospsinp-4sinp$
Now put values of p for each quadrant or from 0 to $2\Pi$
You will see for the common angles like $30^{\circ},60^{\circ},etc.$ the equation will not be satisfied by angles present in 3rd and 4th quadrant or in other words $(\Pi ,2\Pi )$
so, p can be only in 1st and 2nd quadrant
Hence the correct option is (d).
Hope it helps!