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BCECE Engineering BCECE Engineering Solved Paper-2011

  • question_answer
    If the roots of the equation \[a(b-c){{x}^{2}}+b(c-a)x+c(a-b)=0\]are equal, then a, b, c are in

    A)  AP           

    B)                                         GP                         

    C)         HP                                         

    D)         None of these                                                     

    Correct Answer: C

    Solution :

    Since, roots of the equation are equal. \[\therefore \] Discriminant = 0                 i.e., \[{{b}^{2}}{{(c-a)}^{2}}-4ac(b-c)(a-b)=0\]                 \[\Rightarrow \]\[{{b}^{2}}{{(c+a)}^{2}}-4abc(a+c)+4{{a}^{2}}{{c}^{2}}=0\]                 \[\Rightarrow \]\[{{(b(a+c)-2ac)}^{2}}=0\,\,\Rightarrow \,\,\,b=\frac{2ac}{a+c}\]                 \[\Rightarrow \]a, b, c are in HP.      


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