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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 \[{{x}^{2}}+6x+\lambda =0\] and \[3\alpha +2\beta =-20\], then \[\lambda =\]

    A) -8

    B) -16

    C)  16

    D)  8

    Correct Answer: B

    Solution :

    \[\alpha +\beta =-6\] ?..(i)  \[\alpha \beta =\lambda \] ?..(ii) and given \[3\alpha +2\beta =-20\] ?..(iii) Solving (i) and (iii), we get \[\beta =2,\alpha =-8\] Substituting these values in (ii), we get\[\lambda =-16\].


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