Answer:
-4, -2, -3-2i, -3+2i
Step-by-step explanation:
The of the polynomial equation are those values of x, for which f(x)=0.
Consider equation
[tex]f(x)=0\\ \\(x^2+6x+8)(x^2+6x+13)=0[/tex]
By zero product property,
[tex]x^2+6x+8=0\ \text{or}\ x^2+6x+13=0[/tex]
Solve each equation:
1. [tex]x^2+6x+8=0[/tex]
[tex]D=6^2-4\cdot 8=36-32=4\\ \\x_{1,2}=\dfrac{-6\pm \sqrt{4}}{2}=\dfrac{-6\pm 2}{2}=-4,\ -2[/tex]
2. [tex]x^2+6x+13=0[/tex]
[tex]D=6^2-4\cdot 13=36-52=-16=16i^2\\ \\x_{1,2}=\dfrac{-6\pm \sqrt{16i^2}}{2}=\dfrac{-6\pm 4i}{2}=-3-2i,\ -3+2i[/tex]
