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KVPY Sample Paper KVPY Stream-SX Model Paper-6

  • question_answer
    If \[x-=5+4i,\] then \[{{x}^{4}}+9{{x}^{3}}+35{{x}^{2}}-x+4=\]

    A) \[-164\]             

    B) 164

    C) \[-160\]             

    D) 160

    Correct Answer: C

    Solution :

    \[x=-\,5+4i\]      \[\Rightarrow \]   \[{{(x+5)}^{2}}=-16\]
    \[\Rightarrow \]   \[{{x}^{2}}+10x+41=0\]
    \[{{x}^{4}}+9{{x}^{3}}+35{{x}^{2}}-x+4=({{x}^{2}}+10x+41)\]
    \[({{x}^{2}}-x+4)-160\]
    Since \[{{x}^{2}}+10x+41=0\]
    \[\therefore \]      \[{{x}^{4}}+9{{x}^{3}}+35{{x}^{2}}-x+4=-160\]


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