If both the distinct roots of the equation |sinx|2+|sinx|+b=0 in [0,π] are real, then the value of b is
A
[−2,0]
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B
(−2,0)
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C
[−2,0)
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D
None of these
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Solution
The correct option is D(−2,0)
Given,
|sinx|2+|sinx|+b=0
Now
b=−∣sinx∣2−∣sinx∣ given xϵ[0,π] and both the roots of this equation are distinct so the value of ∣sinx∣ can't be (1,1) or (0,0) or any equal pair Thus, Range of b is (−2,0)