Answer:
x = -2, (-1 + √3 i ) / 2 , (-1 - √3 i) / 2.
Step-by-step explanation:
x^3 + 3x^2 + 3x + 2 = 0
f(-2) = -8 + 3*4 - 6 + 2
= -8 + 12 - 6 + 2
= 0
So (x + 2) is a factor . Dividing:
x^2 + x + 1
---------------------------------
x + 2) x^3 + 3x^2 + 3x + 2
x^3 + 2x^2
----------------
x^2 + 3x
x^2 + 2x
-----------
x + 2
x + 2.
----------
Solving x^2 + x + 1:
x = [ - 1 +/- sqrt(1 - 4*1*1) ] / 2
= (-1 + √3 i ) / 2 , (-1 - √3 i) / 2.
