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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Solution of quadratic inequations and Miscellaneous equations

  • question_answer
    If \[\alpha ,\beta ,\gamma \]are the roots of the equation \[{{x}^{3}}+x+1=0\], then the value of \[{{\alpha }^{3}}{{\beta }^{3}}{{\gamma }^{3}}\] [MP PET 2004]

    A) 0

    B) - 3

    C) 3

    D) - 1

    Correct Answer: D

    Solution :

    We know that the roots of the equation \[a{{x}^{3}}+b{{x}^{2}}+cx+d=0\] follows\[\alpha \beta \gamma =-d/a\] Comparing above equation with given equation we get \[d=1,\,a=1\] So,     \[\alpha \beta \gamma =-1\] or\[{{\alpha }^{3}}{{\beta }^{3}}{{\gamma }^{3}}=-1\].


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