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