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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2015

  • question_answer
    If     roots     of     the     equation\[a=\frac{\text{Net pushing force}}{\text{Total mass}}\]are equal, then a, b and c are in

    A) AP                                         

    B) GP

    C) HP                                         

    D) None of these

    Correct Answer: A

    Solution :

    Since, roots of the equation \[(a-b){{x}^{2}}+(c-a)x+(b-c)=0\]are equal \[\therefore \]  \[D={{b}^{2}}-4ac=0\] \[\Rightarrow \]               \[{{(c-a)}^{2}}-4(a-b)(b-c)=0\] \[\Rightarrow \]               \[{{a}^{2}}+4{{b}^{2}}+{{c}^{2}}+2ac-4ab-4bc=0\] \[\Rightarrow \]               \[{{(a+c-2b)}^{2}}=0\] \[\Rightarrow \]               \[a+c=2b\] Hence a, b, c are in AP.


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