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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  a, b and g  are the roots of \[{{x}^{3}}+8=0\], then the equation whose roots are \[{{\alpha }^{2}},{{\beta }^{2}}\]and \[{{\gamma }^{2}}\]is

    A) \[{{x}^{3}}-8=0\]

    B) \[{{x}^{3}}-16=0\]

    C) \[{{x}^{3}}+64=0\]

    D) \[{{x}^{3}}-64=0\]

    Correct Answer: D

    Solution :

    Let\[y={{x}^{2}}\]. Then \[x=\sqrt{y}\] \ \[{{x}^{3}}+8=0\,\,\Rightarrow \,\,{{y}^{3/2}}+8=0\] Þ \[{{y}^{3}}=64\,\,\,\Rightarrow \,\,\,{{y}^{3}}-64=0\] Thus the equation having roots \[{{\alpha }^{2}},{{\beta }^{2}}\] and \[{{\gamma }^{2}}\]is\[{{x}^{3}}-64=0\].


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