JEE Main & Advanced Mathematics Quadratic Equations Question Bank Critical Thinking

  • question_answer 34) The roots of the equation\[4{{x}^{4}}-24{{x}^{3}}+57{{x}^{2}}+18x-45=0\], If one of them is\[3+i\sqrt{6}\], are

    A) \[3-i\sqrt{6},\pm \sqrt{\frac{3}{2}}\]

    B) \[3-i\sqrt{6},\pm \frac{3}{\sqrt{2}}\]

    C) \[3-i\sqrt{6},\pm \frac{\sqrt{3}}{2}\]

    D) None of these

    Correct Answer: C

    Solution :

    \[{{x}^{2}}-6x+15=0\]is quadratic corresponding to roots \[3\pm i\sqrt{6}\] and dividing the given equation by this, we get  \[4{{x}^{2}}-3=0\]Þ \[x=\pm \frac{\sqrt{3}}{2}\].

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