algebraically closed fields & the fundamental theorem of algebra

Question 1

algebraically closed field

Answer 1

every polynomial of degree at least 1 has a root in the field

Question 2

general fundamental theorem of algebra

Answer 2

Let K be a field of characteristic 0 where [K:K^2]=2
K=K^2U(-1)K*^2
K^2+K^2=K^2
Every polynomial in K[x] of odd degree has a root in K
Then F=K[x]/Kx=K(t) (where t^2+1=0) is algebraically closed

Question 3

fundamental theorem of algebra

Answer 3

C is algebraically closed