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Question

If both the distinct roots of the equation open vertical bar sin invisible function application x close vertical bar to the power of 2 end exponent plus open vertical bar sin invisible function application x close vertical bar plus b equals 0 blankinblank open square brackets 0 comma pi close square brackets are real, then the values of b are

  1. open square brackets negative 2 comma blank 0 close square brackets  
  2. open parentheses negative 2 comma blank 0 close parentheses  
  3. open square brackets negative 2 comma blank 0 close parentheses  
  4. None of these  

The correct answer is: open parentheses negative 2 comma blank 0 close parentheses


    Given that open vertical bar sin invisible function application x close vertical bar to the power of 2 end exponent plus open vertical bar sin invisible function application x close vertical bar plus b equals 0
    rightwards double arrow open vertical bar sin invisible function application x close vertical bar equals fraction numerator negative 1 plus-or-minus square root of 1 minus 4 b end root over denominator 2 end fraction blank rightwards double arrow 0 less or equal than fraction numerator negative 1 plus-or-minus square root of 1 minus 4 b end root over denominator 2 end fraction less than 1 blank rightwards double arrow negative 2 less than b less than 0

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