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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2000

  • question_answer
    If \[\alpha ,\beta \]are the roots of the equation x2 + x +1 \[{{x}^{2}}+x+1=0\]and \[\alpha /\beta ,\beta /\alpha \]are roots of the equation \[{{x}^{2}}+px+q=0\]then p equals:

    A)  \[-1\]                                   

    B) \[1\]

    C)  \[-2\]                                   

    D) \[2\]

    Correct Answer: B

    Solution :

    \[{{x}^{2}}+x+1=0\]        \[{{x}^{2}}+px+q=0\] \[\alpha +\beta =-1,\alpha \beta =1\]\[\frac{\alpha }{\beta }+\frac{\beta }{\alpha }=-P\] \[-P=\frac{{{(\alpha +\beta )}^{2}}-2\alpha \beta }{\alpha \beta }\frac{{{\alpha }^{2}}+{{\beta }^{2}}}{\alpha \beta }=-P\] \[-P=\frac{1-2}{1}\]  \[\Rightarrow \]\[P=1\]


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