Let `1,,w^2` be the cube root of unity. The least possible degree of a polynomial with real coefficients having roots `2w ,(2+3w),(2+3w^2),(2-w-w^2)` is _____________.

Answer

5

Explanation

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