Question

Let I, `omega` and `omega^(2)` be the cube roots of unity. The least possible degree of a polynomial, with real coefficients having `2omega^(2), 3 + 4 omega, 3 + 4 omega^(2) ` and `5- omega - omega^(2)` as roots is -
A. 4
B. 5
C. 6
D. 8

Answer 1

Correct Answer - B
`{:("roots"rarr, 2omega^(2),3+4omega,3+4omega^(2),5-omega-omega^(2)),(,alpha,beta,gamma,delta):}`
`delta = 5-(omega + omega^(2)) = 5 - (-1) = 6`
If `alpha = 2omega^(2)` is a root then `2omega` has to be a root too.
total `rarr` min. 5 roots, hence min. degree `rarr 5`.