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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 \[k\in (-\infty ,\,-2)\cup (2,\infty ),\] then the roots of the equation \[{{x}^{2}}+2kx+4=0\] are [DCE 2002]

    A) Complex

    B) Real and unequal

    C) Real and equal

    D) One real and one imaginary

    Correct Answer: B

    Solution :

    Given equation is \[{{x}^{2}}+2kx+4=0\] Put\[k=-3\], \[{{x}^{2}}-6x+4=0\]\[\Rightarrow x=3+\sqrt{5},\,3-\sqrt{5}\] Put k = 3, \[{{x}^{2}}+6x+4=0\]\[\Rightarrow x=-3+\sqrt{5},\,-3-\sqrt{5}\] i.e., Roots are real and unequal.


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