Let 1, $\mathrm{\omega },{\mathrm{\omega }}^2$ be the cube roots of unity. The least possible degree of a polynomial with real coefficients having roots $2\mathrm{\omega },(2+3\mathrm{\omega }),\left(2+3{\mathrm{\omega }}^2\right),\left(2-\mathrm{\omega }-{\mathrm{\omega }}^2\right)$ is __________

Roots are $2\mathrm{\omega },(2+3\mathrm{\omega }),\left(2+3{\mathrm{\omega }}^2\right),\left(2-\mathrm{\omega }-{\mathrm{\omega }}^2\right)$ $2+3\mathrm{\omega }\text{ and }2+3{\mathrm{\omega }}^2$ are conjugate to each other.2$\mathrm{\omega }$ is complex root, then other root must be$2{\mathrm{\omega }}^2$ (as complex roots occur in conjugate pair) $2-\mathrm{\omega }-{\mathrm{\omega }}^2=2-(-1)=3$ which is real.
Hence, least degree of the polynomial is 5.