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

  • question_answer
    If \[\alpha ,\beta \] are the roots of \[(x-a)(x-b)=c,\]\[c\ne 0,\] then the roots of \[(x-\alpha )(x-\beta )+c=0\] shall be  [IIT 1992; MP PET 2000; DCE 2000]

    A) a, c

    B) \[b,c\]

    C) \[a,b\]

    D) \[a+c,b+c\]

    Correct Answer: C

    Solution :

    As given, \[\alpha +\beta =a+b\], \[\alpha \beta =ab-c\]or \[ab=\alpha \beta +c\].  Then the required equation is\[{{x}^{2}}-x(\alpha +\beta )+\alpha \beta +c=0\] \[\Leftrightarrow {{x}^{2}}-x(a+b)+ab=0\], whose roots are a, b.


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