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Question

The equation (cos p−1)x2+(cos p)x+sin p=0 in variable x has real roots, if p belongs to the interval


A

(0,π)

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B

(π2,π2)

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C

(π,0)

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D

(0,2π)

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Solution

The correct option is A

(0,π)


(cos p1)x2+(cos p)x+sin p=0.....(1)

Discriminant of (1) is given by D=cos2p4(cos p1)sin p =cos2p+4(1cos p)sin p

Note that cos2 p0,1 cos p0.
Thus D0 if sinp0p(0,π).


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