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

  • question_answer
    \[\{x\in R:|x-2|\,\,={{x}^{2}}\}=\] [EAMCET 2000]

    A) { - 1, 2}

    B) {1, 2}

    C) { - 1, - 2}

    D) {1, - 2}

    Correct Answer: D

    Solution :

    \[|x-2|\,={{x}^{2}}\]\[\Rightarrow x-2={{x}^{2}}\] or \[2-x={{x}^{2}}\] \[\Rightarrow {{x}^{2}}-x+2=0\] or \[{{x}^{2}}+x-2=0\] \[\Rightarrow {{x}^{2}}+x-2=0\]\[[\because {{x}^{2}}-x+2=0\]does not gives any real root] \[\Rightarrow (x+2)(x-1)=0\,\,\,\Rightarrow x=-2,\,1\].


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