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

  • question_answer
    If one of the roots of  equation \[{{x}^{2}}+ax+3=0\] is 3 and one of the roots of the equation \[{{x}^{2}}+ax+b=0\] is three times the other root, then the value of b is equal to    [J & K 2005]

    A) 3

    B) 4

    C) 2

    D) 1

    Correct Answer: A

    Solution :

    Given, \[{{3}^{2}}+a.3+3=0\]; \[a=-4\] Let roots of equation \[{{x}^{2}}-4x+b=0\] is \[\alpha \] and\[3\alpha \]. \[\alpha +3\alpha =4\]Þ \[4\alpha =4\]Þ \[\alpha =1\] Hence \[1-4+b=0\]Þ \[b=3\]


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