Question

Let p(x) be a polynomial of least possible degree with rational coefficients, having 1/7³ + 1/49³ as one of its roots, then the product of all roots of p(x) = 0 is

(a)  56 

(b)  63

(c)  7

(d)  49

Answer 1

Correct option (a) 56

Explanation:

Let x =  1/7^1/3 + 1/49^1/3

Cubing x³

⇒  x³ = 7 + 49 + 3.7(1/7^1/3 + 1/49^2/3)

⇒  x³ = 56 + 21x

⇒ x³ + 0 x² – 21x – 56 = 0

∴  Product of roots is 56