Question

If $\omega$ is a complex cube root of unity, then the equation whose roots are $2\omega$ and $2{\omega }^2$ is

• A. $x^2+2x+4=0$
• B. $x^2+2\omega x+4=0$
• C. $x^2+2{\omega }^{2}x+4=0$
• D. $x^2-2\omega x+4=0$

Answer 1

The correct option is A $x^2+2x+4=0$

To form an equation, whose roots are $2\omega$ and $2{\omega }^2$ , we have
$x^2-2x({\omega }^2+w)+4{\omega }^3=0$
$\Rightarrow x^2-2x(-1)+4\left(1\right)=0$
$\therefore x^2+2x+4=0$ is the required equation.