Let 1, w, w² be the cube roots of unity. The least possible degree of a polynomial with real coefficients having roots 2w, (2 + 3w), (2 + 3w²), (2 – w – w²), is

$2\omega ,2\overline{\omega }$ are conjugate ;${\text{2+3ω,2+3ω}}^2$ are conjugates, $2-\left(\mathrm{\omega }+{\omega }^2\right)=3$

The equation has  4 non real complex roots and one real roots
$\therefore$minimum 5 roots exist. The least possible degree of the polynomial is 5