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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 roots of the equation \[{{x}^{4}}-8{{x}^{2}}-9=0\] are

    A) \[\pm 3,\ \pm 1\]

    B) \[\pm 3,\ \pm i\]

    C) \[\pm 2,\ \pm i\]  

    D) None of these

    Correct Answer: B

    Solution :

    Equation \[{{x}^{4}}-8{{x}^{2}}-9=0\] Þ  \[{{x}^{4}}-9{{x}^{2}}+{{x}^{2}}-9=0\]Þ  \[{{x}^{2}}({{x}^{2}}-9)+1({{x}^{2}}-9)=0\] Þ  \[({{x}^{2}}+1)({{x}^{2}}-9)=0\Rightarrow x=\pm i,\,\,\pm 3\].


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