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Manipal Engineering Manipal Engineering Solved Paper-2012

  • question_answer
    If the roots of the equation                 \[{{x}^{2}}-2ax+{{a}^{2}}+a-3=0\] are real and less than 3, then

    A) \[a<2\]                

    B) \[2\le a\le 3\]

    C) \[3<a\le 4\]       

    D)        \[a>4\]

    Correct Answer: A

    Solution :

    Let\[f(x)={{x}^{2}}-2ax+{{a}^{2}}+a-3=0\].  Since, \[f(x)\]has real roots both less than 3. Therefore,\[D>0\]and\[f(3)>0\] \[\Rightarrow \]               \[4{{a}^{2}}-4({{a}^{2}}+a-3)>0\] and        \[{{a}^{2}}-5a+6>0\]       \[\Rightarrow \]               \[a<3\]and\[a<2\]or\[a>3\] \[\Rightarrow \]               \[a<2\]


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