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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2006

  • question_answer
    Let co be an imaginary root of\[{{x}^{n}}=1\]. Then \[(5-\omega ){{(5-\omega )}^{2}}....(5-{{\omega }^{n-1}})\]is:

    A)  1                            

    B)         \[\frac{{{5}^{n}}+1}{4}\]

    C)  \[{{4}^{n-1}}\]                 

    D)         \[\frac{{{5}^{n}}-1}{4}\]

    E)  \[{{5}^{n-1}}\]

    Correct Answer: D

    Solution :

    Using \[{{z}^{n}}-1=(z-1)(z-\alpha )....(z-{{\alpha }^{n-1}})\] where \[{{z}^{n}}=1\] \[\therefore \]\[(5-\omega )(5-{{\omega }^{2}})....(5-{{\omega }^{n-1}})=\frac{{{5}^{n}}-1}{4}\]


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