Mathematics - Quadratic Equation Question with Solution | TestHub

$x^3-2x^2+2x-1=0$

$x=1$ satisfying the equation

$\therefore x-1$ is factor of $x^3-2x^2+2x-1$

$=\left(x-1\right)\left(x^2-x+1\right)=0$

$x=1,\frac{{\displaystyle 1+i\sqrt{3}}}{{\displaystyle 2}},\frac{{\displaystyle 1-i\sqrt{3}}}{{\displaystyle 2}}$

$x=1,-{\omega }^2,-\omega$

sum of ${162}^{th}$ power of roots

$={\left(1\right)}^{162}+{\left(-{\omega }^2\right)}^{162}+{\left(-\omega \right)}^{162}$

$=1+{\left(\omega \right)}^{324}+{\left(\omega \right)}^{162}$

$=1+1+1=3$