Mathematics - Complex Number Question with Solution | TestHub

Roots are $2w,(2+3w)\left(2+3w^2\right)\left(2-w-w^2\right)(2+3w)$ and $2+3w^2$ are conjugate each other 2 w is complex root, then other root must be $2{\mathrm{w}}^2$ (as conjugate root occur in conjugate pair)

$2-w-w^2=2-(-1)=3$ which is real.

Hence least degree of the polynomial : 5.