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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2010

  • question_answer
    If   \[a,-a,\] b   are   the   roots   of \[{{x}^{3}}-5{{x}^{2}}-x+5=0,\]  then b is a root of

    A) \[{{x}^{2}}+3x-20=0\]

    B) \[{{x}^{2}}-5x+10=0\]

    C) \[{{x}^{2}}-3x-10=0\]

    D)   \[{{x}^{2}}+5x-30=0\]  

    Correct Answer: C

    Solution :

      Given,   \[{{x}^{3}}-5{{x}^{2}}-x+5=0\]   Here, roots \[(a,-a,b),\]   Sum of the roots \[=a-a+b=5\]                                   \[b=5\]   and \[b=5\] satisfies the equation                   \[f(x)\equiv {{x}^{2}}-3x-10=0\]   i.e,          \[f(5)\equiv {{(5)}^{2}}-3(5)-10\]                   \[=25-15-10\]                   \[=0\]   So, is the roots equation \[{{x}^{2}}-3x-10=0.\]  


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