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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2009

  • question_answer
        If the roots of the quadratic equation\[{{x}^{2}}-4x-lo{{g}_{3}}a=0\]are real, then the least value of a is

    A)  81                                         

    B)  1/81

    C)  1/64                                     

    D)  None of these

    Correct Answer: B

    Solution :

                    Since, the roots of the given equation are real. \[\therefore \]  \[Disc>0\Rightarrow 16+4\text{ }lo{{g}_{3}}a\ge 0\] \[\Rightarrow \]               \[{{\log }_{3}}a\ge -4\Rightarrow a\ge {{3}^{-4}}\Rightarrow a\ge 1/81\] Hence, the least value of a is\[1/81\].


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