Answer:
[tex]x_4 = -5 + i[/tex]
Step-by-step explanation:
See comment for complete question.
From the complete question, we have:
[tex]Zeros \to -2, -6, -5-i[/tex]
Required
Determine the other zero
The zeros can be represented as:
[tex]x_1 = -2[/tex]
[tex]x_2 = -6[/tex]
[tex]x_3 = -5-i[/tex]
Considering the 3rd zero, which is a complex number.
If a polynomial has a complex number as one of its zeros, then its conjugate pair is the corresponding zero
A conjugate pair is given as:
[tex]a + bi[/tex] and [tex]a - bi[/tex]
For [tex]x_3 = -5-i[/tex]
The conjugate pair is:
[tex]x_4 = -5 + i[/tex]
Hence, the other zero is: [tex]-5 + i[/tex]
