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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 \[{{x}^{2}}-6x+a=0\] and satisfy the relation \[3\alpha +2\beta =16,\]then the value of a is

    A) - 8

    B) 8

    C) - 16

    D) 9

    Correct Answer: B

    Solution :

    \[3\alpha +2\beta =16\,\,\,\Rightarrow \,\,2(\alpha +\beta )+\alpha =16\] Þ \[2\times 6+\alpha =16\,\,\,\Rightarrow \,\,\alpha =4\] \ \[{{4}^{2}}-6\times 4+a=0\,\,\,\Rightarrow \,a=8\].


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