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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
    \[{{x}^{2}}+x+1+2k\,({{x}^{2}}-x-1)=0\]is a perfect square for how many values of k [Orissa JEE 2004]

    A) 2

    B) 0

    C) 1

    D) 3

    Correct Answer: A

    Solution :

    Given equation \[(1+2k){{x}^{2}}+(1-2k)x+(1-2k)=0\] If equation is a perfect square then root are equal i.e.,  \[{{(1-2k)}^{2}}-4(1+2k)\,(1-2k)\,=0\] i.e.,  \[k=\frac{1}{2},\,\frac{-3}{10}\]. Hence total number of values = 2.


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