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, \[{{x}^{4}}+9{{x}^{3}}+35{{x}^{2}}-x+4\] \[=({{x}^{2}}+10x+41)({{x}^{2}}-x+4)-160=-160\]


You need to login to perform this action.
You will be redirected in 3 sec spinner