Which of the following is the complete list of roots for he polynomial function f (x) = (x^2+6x+8) (x^2+6x+13)

Answer: the list of roots is {-4, 2, - 3+2i, - 3-2i}

Use the quadratic formula to get the roots of the two separate terms in brackets:

x^2+6x+8=0 has solutions: - 4 and 2

x^2+6x+13=0 has solutions: - 3+2i and - 3-2i

The complete roots of the function are. Option (C) is correct.

Further explanation:

The Fundamental Theorem of Algebra states that the polynomial has n roots if the degree of the polynomial is n.

The polynomial function has roots or zeroes.

Given:

The function is

Explanation:

To obtain the roots of the polynomial function substitute for either the value of or

Solve the function to obtain the zeroes.

Solve the function to obtain the zeroes.

The roots can be obtained as follows,

The complete roots of the function are Option (C) is correct.