Question

If $1,\omega$ and ${\omega }^2$ are cube root of unity,then their product is

• A. $0$
• B. $\omega$
• C. $1$
• D. $-1$

Answer 1

The correct option is C $1$

$1,\omega ,{\omega }^2$ are roots of $x^3-1=0$

Product of roots= $1\times \omega \times {\omega }^2$

$=-\frac{\text{Constant in Cubic Polynomial}}{\text{Coefficient of x with power 3 in Quadratic polynomal}}$

$=-\left(\frac{-1}{1}\right)$

Product of roots$=1$