Equation `x^(n)-1=0, ngt1, n in N," has roots "1,a_(1),a_(2),…,a_(n-1).`
The value of `(1-a_(1))(1-a_(2))…(1-a_(n-1))` is

Options

A. `n^(2)//2`
B. n
C. `(-1)^(n)n`
D. none of these

Explanation

To solve the problem, we need to find the value of \((1 - a_1)(1 - a_2) \ldots (1 - a_{n-1})\) where the roots of the equation \(x^n - 1 = 0\) are \(1, a_1, a_2, \ldots, a_{n-1}\).

### Step-by-step Solution:

1. **Identify the Roots of the Equation**:
The equation \(x^n - 1 = 0\) can be factored as:
\[
x^n - 1 = (x - 1)(x - a_1)(x - a_2) \ldots (x - a_{n-1})
...