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

  • question_answer
    If \[\alpha \] and \[\beta \] are the roots of the equation \[{{x}^{2}}-4x+1=0\] the value of \[{{\alpha }^{3}}+{{\beta }^{3}}\]is [MP PET 1994]

    A) 76

    B) 52

    C) -52

    D) -76

    Correct Answer: B

    Solution :

    \[{{\alpha }^{3}}+{{\beta }^{3}}={{(\alpha +\beta )}^{3}}-3\alpha \beta (\alpha +\beta )\]               \[={{(4)}^{3}}-3\times 1(4)=52\]


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