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  5. Complex Numbers and Quadratic Equations

11th Class Mathematics Complex Numbers and Quadratic Equations Question Bank Critical Thinking

  • question_answer
    If \[x=-5+2\sqrt{-4},\] then the value of the expression  \[{{x}^{4}}+9{{x}^{3}}+35{{x}^{2}}-x+4\] is [IIT 1972]

    A) 160

    B) \[-160\]

    C) 60

    D) \[-60\]

    Correct Answer: B

    Solution :

    \[x+5=4i\]Þ \[{{x}^{2}}+10x+25=-16\] Now, \[{{x}^{4}}+9{{x}^{3}}+35{{x}^{2}}-x+4\] \[=({{x}^{2}}+10x+41)({{x}^{2}}-x+4)-160=-160\]


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