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Manipal Engineering Manipal Engineering Solved Paper-2011

  • question_answer
    If the roots of the equation\[\frac{\alpha }{x-\alpha }+\frac{\beta }{x-\beta }=1\]be equal in magnitude but opposite in sign, then\[\alpha +\beta \]is equal to

    A)  0                                            

    B)  1

    C)  2                            

    D)         None of these

    Correct Answer: A

    Solution :

    Given equation can be rewritten as                 \[{{x}^{2}}-2(\alpha +\beta )x+3\alpha \beta =0\] Let roots be\[\alpha \]and\[-\alpha \]. \[\therefore \]  \[\alpha +(-\alpha )=2(\alpha +\beta )\] \[\Rightarrow \]               \[\alpha +\beta =0\]


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