for the equation `|{:(1,,x,,x^(2)),(x^(2),,1,,x),(x,,x^(2),,1):}|=0`

Options

A. There are exactly two distinct roots
B. there is one pair of equation real roots
C. There are three pairs of equal roots
D. Modulus of each root is 2

Answer

C

Explanation

`Delta = (1+ x+x^(2)) |{:(1,,1,,1),(x^(2),,1,,x),(x,,x^(2),,1):}| =(1-x^(3))^(2)`
Therefore `Delta =0` has roots `1,1 ,omega, omega, omega^(2),omega^(2)`