JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Solution of quadratic equations and Nature of roots

  • question_answer
    The value of  \[x=\sqrt{2+\sqrt{2+\sqrt{2+.....}}}\]is  [Karnataka CET 2001]

    A) -1

    B) 1

    C) 2

    D) 3

    Correct Answer: C

    Solution :

    \[x=\sqrt{2+x}\] Þ \[{{x}^{2}}-x-2=0\] Þ \[(x-2)(x+1)=0\] Þ  \[x=2,-1\] But\[\sqrt{2+\sqrt{2+.....}}\ne -1\], so it is equal to 2.


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