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JEE Main & Advanced Mathematics Sets Question Bank Mock Test - Sets

  • question_answer
    Number of integers satisfying the inequality, \[{{x}^{4}}-29{{x}^{2}}+100\le 0\]is

    A) 2                     

    B) 4

    C) 6                     

    D) 8

    Correct Answer: D

    Solution :

    [d] we have \[{{x}^{4}}-29{{x}^{2}}+100\le 0\] \[\Rightarrow \]   \[({{x}^{2}}-4)({{x}^{2}}-25)\le 0\] \[\Rightarrow \]   \[4\le {{x}^{2}}\le 25\] \[\Rightarrow \]   \[x\in [-5,-2]\cup [2,5]\] Integers satisfying above are \[\pm \]5,\[\pm \]4,\[\pm \]3,\[\pm \]2. So there are eight integers.


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