Answer:
x=-1 x = ±2i
Step-by-step explanation:
x^3+x^2+4x+4=0
Factor by grouping
x^3 + x^2 + 4x+4 =0
Factor and x^2 from the first group and 4 from the second group
x^2(x+1) +4(x+1)
Factor out the x+1
(x+1) (x^2+4) = 0
Using the zero product property
x+1 = 0 x^2 +4= 0
x=-1 x^2 = -4
Taking the square root of each side
sqrt(x^2) = ±sqrt(-4)
We know that sqrt(ab) = sqrt(a) sqr(b)
sqrt(x^2) =±sqrt(-1) sqrt(4)
x= ±i * 2
x=-1 x = ±2i
