JEE Main & Advanced Mathematics Quadratic Equations Question Bank Critical Thinking

  • question_answer If the equation \[{{x}^{2}}+\lambda x+\mu =0\] has equal roots and one root of the equation \[{{x}^{2}}+\lambda x-12=0\]is 2, then \[(\lambda ,\mu )\]=

    A) (4, 4)

    B) (-4,4)

    C) \[(4,-4)\]

    D) \[(-4,-4)\]

    Correct Answer: A

    Solution :

    We have equal roots, therefore\[{{\lambda }^{2}}=4\mu \]. Now second equation \[{{x}^{2}}+\lambda x-12=0\] has a root 2, so put \[x=2\]Þ \[4+2\lambda -12=0\]Þ \[\lambda =4\] Hence from\[{{\lambda }^{2}}=4\mu \], we have \[\mu =\frac{16}{4}=4\]  Þ \[(\lambda ,\mu )=(4,4)\].

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