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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Relation between roots and coefficients

  • question_answer
    If \[\alpha \] and \[\beta \] are the roots of the equation \[{{x}^{2}}-a(x+1)-b=0\] then \[(\alpha +1)(\beta +1)=\]

    A) b

    B) - b

    C) \[1-b\]

    D) \[b-1\]

    Correct Answer: C

    Solution :

    Given equation \[{{x}^{2}}-a(x+1)-b=0\] Þ \[{{x}^{2}}-ax-a-b=0\]Þ \[\alpha +\beta =a,\alpha \beta =-(a+b)\] Now \[(\alpha +1)(\beta +1)=\alpha \beta +\alpha +\beta +1\]                                     = \[-(a+b)+a+1=1-b\]


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