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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Solution of quadratic equations and Nature of roots

  • question_answer
    The number of solutions of \[\frac{\log 5+\log ({{x}^{2}}+1)}{\log (x-2)}=2\] is

    A) 2

    B) 3

    C) 1

    D) None of these

    Correct Answer: D

    Solution :

    We have \[\frac{\log 5+\log ({{x}^{2}}+1)}{\log (x-2)}=2\] Þ \[\log \{5({{x}^{2}}+1)\}=\log {{(x-2)}^{2}}\Rightarrow 5({{x}^{2}}+1)={{(x-2)}^{2}}\] \[\Rightarrow \] \[4{{x}^{2}}+4x+1=0\Rightarrow x=-\frac{1}{2}\] But for \[x=-\frac{1}{2}\log (x-2)\] is not meaningful. Hence it has no root.


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