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 = 1/71/3 + 1/491/3

Cubing x3

⇒x3 = 7 + 49 + 3.7(1/71/3 + 1/492/3)

⇒x3 = 56 + 21x

⇒x3+ 0 x2– 21x – 56 = 0

∴ Product of roots is 56