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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  \[{{x}^{2}}-3x+2\]be a factor of \[{{x}^{4}}-p{{x}^{2}}+q,\]then \[(p,q)=\]   [IIT 1974; MP PET 1995; Pb. CET 2001]

    A) (3, 4)

    B) (4, 5)

    C) (4, 3)

    D) (5, 4)

    Correct Answer: D

    Solution :

    \[{{x}^{2}}-3x+2\]be factor of \[{{x}^{4}}-p{{x}^{2}}+q=0\] Hence \[({{x}^{2}}-3x+2)=0\,\,\Rightarrow (x-2)(x-1)=0\] Þ \[x=2,\,1,\]putting these values in given equation so  \[4p-q-16=0\] .....(i) and \[p-q-1=0\] .....(ii) Solving (i) and (ii), we get (p, q)=(5, 4)


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