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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 18

  • question_answer
    The number of real roots of the following equation \[|x{{|}^{2}}-7|x|+12=0\]

    A) 1

    B)   2         

    C) 3        

    D)   4

    Correct Answer: D

    Solution :

    Given equation :  \[|x{{|}^{2}}-7|x|+12=0\] We know that \[|x{{|}^{2}}={{x}^{2}},\]so the given equation may be written as  \[{{x}^{2}}-7|x|+12=0\] If \[x<0,\] \[{{x}^{2}}+7x+12=0\]     \[[\because \,\,|x|=-x\,\,if\,\,x<0]\] \[\Rightarrow \,\,\,(x+4)\,\,(x+3)=0\] \[\Rightarrow \,\,\,x=-3,-4\] and, further If  \[x>0\] \[{{x}^{2}}-7x+12=0\]       \[[\because \,\,|x|=x,\,\,if\,x>0]\] \[\Rightarrow \,\,(x-4)\,(x-3)=0\Rightarrow x=3,4\] \[\therefore \]  No. of roots = 4


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