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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 both the roots of \[k(6{{x}^{2}}+3)+rx+2{{x}^{2}}-1=0\] and \[6k(2{{x}^{2}}+1)+px+4{{x}^{2}}-2=0\] are common, then \[2r-p\] is equal to [MNR 1983]

    A) -1

    B) 0

    C) 1

    D) 2

    Correct Answer: B

    Solution :

    Given equation can be written as \[(6k+2){{x}^{2}}+rx+3k-1=0\]         .....(i) and \[2(6k+2){{x}^{2}}+px+2(3k-1)=0\]      .....(ii) Condition for common roots is \[\frac{12k+4}{6k+2}\]\[=\frac{p}{r}=\frac{6k-2}{3k-1}=2\]or \[2r-p=0\]


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