With out using a calculator, find all the roots of the equation. X^3+x^2+4x+4=0?

A. 1,+i

B. 2,3+i

C. + 3,1

D. - 1,+2i

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