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

  • question_answer
    The equation whose roots are reciprocal of the roots of the equation \[3{{x}^{2}}-20x+17=0\] is [DCE  2002]

    A) \[3{{x}^{2}}+20x-17=0\]

    B) \[17{{x}^{2}}-20x+3=0\]

    C) \[17{{x}^{2}}+20x+3=0\]

    D) None of these

    Correct Answer: B

    Solution :

    Given equation is \[3{{x}^{2}}-20x+17=0\] Þ  \[(x-1)(3x-17)=0\]Þ \[x=1,\,\,\frac{17}{3}\] Reciprocal roots are 1 and \[\frac{3}{17}\] \ Equation is \[{{x}^{2}}-\left( 1+\frac{3}{17} \right)\,x+\frac{3}{17}=0\] Þ \[17{{x}^{2}}-20x+3=0\].


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