Question 363587
Solution: Let x = -2 .Plug in this in the given polynomial

x^4+4x^3+5x^2+4x+4
(-2)^4 + 4 (-2)^3+5(-2)^2 +4(-2)+ 4=16-32+20-8+4=0
so x = -2 is a root and (x+2) is a factor
Let us divide the given polynomial with (x+2)
we get 
x^3+2x^2+x+2 
again  plug in x = -2
so (x+2) is a factor again and divide x^3+2x^2+x+2 by (x+2)
we get x^2 + 1 after division
and the roots of x^2 +1 = 0 are x = + i and x = -i
so the roots are 

x = -2 repeated twice
so there are two real roots
-2 and -2
and there are two complex roots .They are i and -i