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

`"Since "1,a_(1),a_(2),...,a_(n-1)" are roots of "x^(n)-1=0,"we have "`
`x^(n-1)=(x-1)(x-a_(1))(x-a_(2))...(x-a_(n-1))" (1)"`
`"or "(x^(n)-1)/(x-1)=(x-a_(1))(x-a_(2))...(x-a_(n-1))`
`"or "underset(xrarr1)lim(x^(n)-1)/(x-1)=underset(xrarr1)lim[(x-a_(1))(x-a_(2))...(x-a_(n-1))]`
`"or "(1-a_(1))(1-a_(2))...(1-a_(n-1))=n`