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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 the roots of the equation \[a{{x}^{2}}+x+b=0\] be real, then the roots of the equation \[{{x}^{2}}-4\sqrt{ab}x+1=0\] will be

    A) Rational

    B) Irrational

    C) Real

    D) Imaginary

    Correct Answer: D

    Solution :

    \[a{{x}^{2}}+x+b=0\]has real roots Þ \[{{(1)}^{2}}-4ab\ge 0\,\,\,\Rightarrow -4ab\ge -1\]or \[4ab\le 1\] .....(i) Now second equation is \[{{x}^{2}}-4\sqrt{ab}x+1=0\] Therefore \[D=16ab-4,\]from (i) \[D\le 0\] Hence roots are imaginary.


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