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Manipal Engineering Manipal Engineering Solved Paper-2010

  • question_answer
    If\[a,\,\,b,\,\,c\]are three distinct positive real numbers of real roots of\[a{{x}^{2}}+2b|x|-c=0\]is

    A)  4                                            

    B)  2

    C)  0                            

    D)         None of these

    Correct Answer: B

    Solution :

    \[a{{x}^{2}}+2b|x|-c=0\] \[\Rightarrow \]               \[a|x{{|}^{2}}+2b|x|-c=0\] \[\therefore \]\[|x|\,\,=\frac{-2b\pm \sqrt{4{{b}^{2}}+4ac}}{2}=-b\pm \sqrt{{{b}^{2}}+ac}\] Since,\[a,\,\,b,\,\,c\]are positive. So,                 \[|x|=-b+\sqrt{{{b}^{2}}+ac}\] \[\therefore \]\[x\]has two real values, neglecting \[|x|=-b-\sqrt{{{b}^{2}}+ac}\], as\[|x|\,\,>0\]


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