Multiple choice

If 1, α1, α2, ... αn - 1 are the roots of the equation xn _ 1 = 0, the value of (1 - α1)(1 - α2)(1 - α3) ... (1 - αn - 1) is

  1. 0

  2. 1

  3. n

  4. n2
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C Correct answer
Explanation

For x^n - 1 = 0, the product over all roots except 1 is obtained from the factorization (x^n - 1)/(x - 1). Evaluating this quotient at x = 1 gives n.

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