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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Condition for common roots, Quadratic expressions and Position of roots

  • question_answer
    If the equation \[{{x}^{2}}+px+q=0\] and \[{{x}^{2}}+qx+p=0\], have a common root, then \[p+q+1=\] [Orissa JEE 2002]

    A) 0

    B) 1

    C) 2

    D) - 1

    Correct Answer: A

    Solution :

    Let a  is the common root, so \[{{\alpha }^{2}}+p\alpha +q=0\]  .....(i) and \[{{\alpha }^{2}}+q\alpha +p=0\]                                    ....(ii) from (i) - (ii), \[\Rightarrow (p-q)\alpha +(q-p)=0\]\[\Rightarrow \alpha =1\] Put the value of \[\alpha \]in (i), \[p+q+1=0.\]


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