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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Mock Test - Complex Numbers and Quadratic Equations

  • question_answer
    Let p(x) =0 be a polynomial equation of the least possible degree, with rational coefficients, having \[\sqrt[3]{7}+\sqrt[3]{49}\]as one of its roots. Then the product of all the roots of p(x)=0 is

    A) 56                   

    B) 63

    C) 7                    

    D) 49

    Correct Answer: A

    Solution :

    [a] \[x=\sqrt[3]{7}+\sqrt[3]{49}\] \[\Rightarrow {{x}^{3}}=7+49+3\sqrt[3]{7}\sqrt[3]{49}(\sqrt[3]{7}+\sqrt[3]{49})=56+21x\] Or \[{{x}^{3}}-21x-56=0\] Therefore, the product of roots is 56.


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