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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 given equation \[2({{a}^{2}}+{{b}^{2}}){{x}^{2}}+2(a+b)x+1=0\] are

    A) Rational

    B) Irrational

    C) Real

    D) Imaginary

    Correct Answer: D

    Solution :

    Given equation \[2({{a}^{2}}+{{b}^{2}}){{x}^{2}}+2(a+b)x+1=0\] Let \[A=2({{a}^{2}}+{{b}^{2}}),B=2(a+b)\]and \[C=1\] \[{{B}^{2}}-4AC=4({{a}^{2}}+{{b}^{2}}+2ab)-4\,.2({{a}^{2}}+{{b}^{2}})\,1\] \[\Rightarrow {{B}^{2}}-4AC=-4{{(a-b)}^{2}}<0\] Thus given equation has imaginary roots.


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