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Manipal Engineering Manipal Engineering Solved Paper-2012

  • question_answer
    The harmonic mean of the root of the equation\[(5+\sqrt{2}){{x}^{2}}-(4+\sqrt{5})x+8+2\sqrt{5}=0\]is

    A)  2                            

    B)  4

    C)  6               

    D)                         8

    Correct Answer: B

    Solution :

                    Let\[\alpha ,\,\,\beta \]be the roots of given quadratic equation. Then,                 \[\alpha +\beta =\frac{4+\sqrt{5}}{5+\sqrt{2}}\]and\[\alpha \beta =\frac{8+2\sqrt{5}}{5+\sqrt{2}}\] Again,\[H\]be the harmonic mean between a and\[\beta \], then\[H=\frac{2\alpha \beta }{\alpha +\beta }=\frac{16+4\sqrt{5}}{4+\sqrt{5}}=4\]


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