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

  • question_answer
    If one root of the equation \[{{x}^{2}}+px+q=0\] is \[2+\sqrt{3}\], then values of p and q are [UPSEAT  2002]

    A) - 4, 1

    B) 4, - 1

    C) 2, \[\sqrt{3}\]

    D) \[-2,\,\,-\sqrt{3}\]

    Correct Answer: A

    Solution :

    One root is \[2+\sqrt{3}\], then second root must be  \[2-\sqrt{3}.\] Þ Sum of roots \[=-p=[2+\sqrt{3}+2-\sqrt{3}]=4\]Þ p = - 4 and product of roots \[=q=(2+\sqrt{3})(2-\sqrt{3}]=4-3=1\] Þ \[(p,q)=(-4,\,\,1)\].


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