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JEE Main & Advanced Mathematics Sequence & Series Question Bank Relation between AP., GP. and HP.

  • question_answer
    If A is the A.M. of the roots of the equation \[{{x}^{2}}-2ax+b=0\] and \[G\] is the G.M. of the roots of the equation \[{{x}^{2}}-2bx+{{a}^{2}}=0,\] then [UPSEAT 2001]

    A) \[A>G\]

    B) \[A\ne G\]

    C) \[A=G\]

    D) None of these

    Correct Answer: C

    Solution :

    Sum of the roots of \[{{x}^{2}}-2ax+{{b}^{2}}=0\] is 2a, Therefore, A = A.M. of the roots = a. Product of the roots of \[{{x}^{2}}-2bx+{{a}^{2}}=0\,\,\text{is}\,\,\,{{a}^{2}}\] Therefore, G.M. of the roots is \[G=a\] Thus,\[A=G\]


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