Question

Which of the following is the complete list of roots for the polynomial function f (x) = (x2 + 6x + 8) (x2 + 6x + 13)?

Answer 1

C

Explanation:

Answer 2

-2, -4, -3 + 2i, -3-2i

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