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

  • question_answer
    If \[2+i\sqrt{3}\] is a root of the equation \[{{x}^{2}}+px+q=0\], where p and q are real, then \[(p,q)\]= [IIT 1981; MP PET 1997, 2004]

    A) \[(-4,\,7)\]

    B) \[(4,\,-7)\]

    C) (4, 7)

    D) \[(-4,\,\,-7)\]

    Correct Answer: A

    Solution :

    Since \[2+i\sqrt{3}\] is a root, therefore \[2-i\sqrt{3}\] will be other root. Now sum of the roots \[=4=-p\] and product of roots \[=7=q\]. Hence \[(p,q)=(-4,7)\].


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