Question

Consider the following properties which are related to equations and their roots:
A. If \(1,\alpha,\beta,\gamma\) are roots of \(x^4-1=0\), then \((1-\alpha)(1-\beta)(1-\gamma)=0\),
B. If \(1,\alpha,\beta,\gamma\) are roots of \(x^4-1=0\), then \((1-\alpha)(1-\beta)(1-\gamma)=4\),
C. If \(\omega,\omega^2,\omega^3,\ldots,\omega^{n-1}\) are the imaginary roots of unity, then \((1-\omega)(1-\omega^2)\cdots(1-\omega^{n-1})=n-1\),
D. If \(\omega,\omega^2,\omega^3,\ldots,\omega^{n-1}\) are the imaginary roots of unity, then \((1-\omega)(1-\omega^2)\cdots(1-\omega^{n-1})=n\).

• A. A, C
• B. B, D
• C. A, D
• D. B, C

Hint:

For \(n\)th roots of unity, \((1-\omega)(1-\omega^2)\cdots(1-\omega^{n-1})=n\).

Answer 1

The Correct Option is B