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

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

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Grade:12th pass

1 Answers

Soumendu Majumdar
159 Points
5 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!

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