Question

Let p(x) = 0 be a polynomial equation of least possible degree, with rational coefficients, having $\sqrt[3]{37}+\sqrt[3]{349}$ as one of its roots. Then the product of all the roots of p(x) = 0 is

• A. 49
• B. 63
• C. 7
• D. 56

Answer 1

The correct option is D 56

$x=7^{\frac{1}{3}}+7^{\frac{2}{3}}$
$x^3=7+49+3.7(7^{\frac{1}{3}}+7^{\frac{2}{3}})$
$x^3=56+21x$
$x^3-21x-56=0$
product of root = 56