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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 number of solutions for the equation \[{{x}^{2}}-5|x|+\,6=0\] is [Karnataka CET 2004]

    A) 4

    B) 3

    C) 2

    D) 1

    Correct Answer: A

    Solution :

    Given equation \[{{x}^{2}}-5|x|+6=0\] i.e.,  \[{{x}^{2}}-5x+6=0\] and \[{{x}^{2}}+5x+6=0\] \[{{x}^{2}}-3x-2x+6=0\] and \[{{x}^{2}}+3x+2x+6=0\] \[(x-3)\,(x-2)=0\] and \[(x+3)\,.\,(x+2)=0\] \[x=3,x=2\] and \[x=-3,\,x=-2\]. i.e.,  Four solutions of this equation.


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