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11th Class Mathematics Complex Numbers and Quadratic Equations Question Bank Critical Thinking

  • question_answer
    The product of all real roots of the equation \[{{x}^{2}}-|x|-\,6=0\] is [Roorkee 2000]

    A) - 9

    B) 6

    C) 9

    D) 36

    Correct Answer: A

    Solution :

    Given equation \[{{x}^{2}}-|x|-6=0\] If\[x>0\], \ equation is \[{{x}^{2}}-x-6=0\] Þ \[(x-3)(x+2)=0\]  Þ  \[x=3,\,x=-2\]  Þ \[x=3\] If\[x<0\],  \ equation is \[{{x}^{2}}+x-6=0\] Þ \[(x+3)(x-2)=0\] Þ  \[x=-3,\,x=2\]  Þ  \[x=-3\] Hence product of all possible real roots = - 9.


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