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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
    If a and b are the odd integers, then the roots of the equation \[2a{{x}^{2}}+(2a+b)x+b=0,\ a\ne 0,\] will be [Pb. CET 1988]

    A) Rational

    B) Irrational

    C) Non-real

    D) Equal

    Correct Answer: A

    Solution :

    Given equation \[2a{{x}^{2}}+(2a+b)x+b=0\],  \[(a\ne 0\]) Now its discriminant \[D={{B}^{2}}-4AC\] \[={{(2a+b)}^{2}}-4.2ab={{(2a-b)}^{2}}\] Hence D is a perfect square, so given equation has rational roots.


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