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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2004

  • question_answer
    The number of solutions for the equation\[{{x}^{2}}-5\,|x|+6=0\] is :

    A)  4                                            

    B)  3

    C)  2                                            

    D)  1

    Correct Answer: A

    Solution :

    Case I: \[|x|=-x\] \[\therefore \]  \[{{x}^{2}}+5x+6=0\]                 \[{{x}^{2}}+3x+2x+6=0\]                 \[x(x+3)+2(x+3)=0\] \[\therefore \]  \[(x+2)\,(x+3)=0\] \[\Rightarrow \]                               \[x=-2,\,-3\] Case II: \[|x|=x\] \[\therefore \]  \[{{x}^{2}}-5x+6=0\]                 \[{{x}^{2}}-3x-2x+6=0\]                 \[x\,(x-3)-2\,(x-3)=0\]                 \[(x-2)(x-3)=0\] \[\Rightarrow \]                                               \[x=2,3\] Hence, there are four roots \[i.e.,\,\,\pm 2,\pm 3\] \[\therefore \] There are four solutions.


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