2010/016) Let 1, a1, ... ,a6 denote the distinct roots of x^7 - 1.

Let 1, a1, ... ,a6 denote the distinct roots of x^7 - 1. Then the product (1 - a1)(1 - a2)(1 - a3) ...(1 - a6) is

is
a) 0;
b) 1;
c) 6;
d) 7;
Kindly explain...
x^7- 1 = (x-1)(x-a1)(x-a2)(x-a3)(x-a4)(x-a5)(x-a6… by definition of roots

dividing by (x-1) on both sides

x^6+x^5+x^4+x^3+x^2+x+1 = (x-a1)(x-a2)(x-a3)(x-a4)(x-a5)(x-a6)

putting x= 1 on both sides we get 7 = (1-a1)(1-a2)(1-a3)(1-a4)(1-a5)(1-a6)

hence d