Answer:
-2, -4, -3 + 2i, -3-2i
Step-by-step explanation:
Equaling the function to zero we have:
(x ^ 2 + 6x + 8) (x ^ 2 + 6x + 13) = 0
For the first parenthesis we have:
(x ^ 2 + 6x + 8) = 0\\(x + 4) (x + 2) = 0
Therefore the roots are:
x = - 4\\x = - 2
For the second parenthesis we have:
(x ^ 2 + 6x + 13) = 0
By completing squares we have:
x ^ 2 + 6x = -13
x ^ 2 + 6x + (\frac{6}{2}) ^ 2 = -13 + (\frac{6}{2}) ^ 2\\x ^ 2 + 6x + 9 = -13 + 9\\(x + 3) ^ 2 = - 4\\x + 3 = +/- \sqrt{-4}
Therefore the roots are:
x = -3 + 2i\\x = -3 - 2i
Hope this was helpful
