Question

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

Answer 1

x=-1 x = ±2i

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