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10th Class Mathematics Related to Competitive Exam Question Bank Quadratic Inequation

  • question_answer
    If \[\frac{{{m}^{2}}+m-6}{{{m}^{2}}+m-2}<0\], then which of the following is true?

    A)  \[1<m<3\]                  

    B)  \[-3<m<-2\]

    C)  \[m\in (-3,-2)\cup (1,2)\] 

    D)  None of these

    Correct Answer: C

    Solution :

    (c): \[\frac{{{m}^{2}}+m-6}{{{m}^{2}}+m-2}<0\Rightarrow \frac{(m+3)(m-2)}{(m-1)(m+2)}<0\] \[\Rightarrow \frac{(m+3)(m-2)(m-1)(m+2)}{{{(m-1)}^{2}}{{(m+2)}^{2}}}<0\] (multiplying numerator and denominator by (m - 1) (m+2) \[\Rightarrow (m+3)(m-2)(m-1)(m+2)<0\] \[\Rightarrow (m-2)(m-1)(m+2)(m+3)<0\] \[\Rightarrow m\in (-3,-2)\cup (1,2)\]


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