Let p(x)=0 be a polynomial equation of least possible degree, with rational coefficients, having 71/3+491/3 as one of its roots. Then the product of all the roots of p(x)=0 is
A
7
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B
49
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C
56
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D
63
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Solution
The correct option is C56 ⇒x=3√7+3√49 --- [ Given ]
⇒x3=(3√7+3√49)3
⇒x3=(3√7)3+(3√49)3+3×(7)1/3(7)2/3(3√7+3√49)
⇒x3=7+49+3×7(3√7+3√49)
⇒x3=56+3×(x)
⇒x3=56+3x
⇒x3−3x−56=0
⇒This gives a cubic polynomial in x and product of roots =56