KVPY Sample Paper KVPY Stream-SX Model Paper-29

  • question_answer
    The value of K such that sum of the squares of the roots of quadratic equation,\[{{x}^{2}}+(3-\lambda )x+2=\lambda \] has the lest value is:

    A) \[\frac{15}{8}\]

    B) \[1\]

    C) \[\frac{4}{9}\]  

    D) \[2\]

    Correct Answer: D

    Solution :

    \[{{\alpha }^{2}}+{{\beta }^{2}}=(\alpha +{{\beta }^{2}})-2\alpha \beta \]
    \[={{(3-\lambda )}^{2}}-2(2-\lambda )\]
    \[={{\lambda }^{2}}+9-6\lambda -4+2\lambda \]
    \[={{\lambda }^{2}}-4\lambda +5\]
    \[\therefore \]For least value\[\lambda =2.\]

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