If both the distinct roots of the equation - sin x -2- - sin x -b-0 in - 0- - are real- then the value of b is

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Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

If both the d...

Question

If both the distinct roots of the equation ${| sin x |}^{2} + | sin x | + b = 0$ in $[0, π]$ are real, then the value of $b$ is

[- 2, 0]

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(- 2, 0)

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[- 2, 0)

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None of these

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Solution

The correct option is D $(- 2, 0)$
Given,
${| sin x |}^{2} + | sin x | + b = 0$

Now
$b = - ∣ s i n x ∣^{2} - ∣ s i n x ∣$
given $x ϵ [0, π]$ and both the roots of this equation are distinct
so the value of $∣ s i n x ∣$ can't be $(1, 1)$ or $(0, 0)$ or any equal pair
Thus, Range of b is $(- 2, 0)$

Hence, option 'B' is correct.

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If both the distinct roots of the equation |sinx|2+|sinx|+b=0 in [0,π] are real, then the value of b is

The correct option is D (−2,0)Given,|sinx|2+|sinx|+b=0Nowb=−∣sinx∣2−∣sinx ∣given xϵ[0,π] and both the roots of this equation are distinctso the value of ∣sinx∣ can't be (1,1) or (0,0) or any equal pairThus, Range of b is (−2,0)Hence, option 'B' is correct.

If both the distinct roots of the equation ${| sin x |}^{2} + | sin x | + b = 0$ in $[0, π]$ are real, then the value of $b$ is