Answer:
The remaining zeros of f is (2 - i) and (-3 + i).
Step-by-step explanation:
We are given a degree six polynomial f and four of its zeros:
[tex]\displaystyle x = -1, 2+i, -3-i, 0[/tex]
And we want to find the remaining zeros of f.
By the Fundamental Theorem of Algebra, the number of zeros of any polynomial is equal to its degree.
Hence, a sixth degree polynomial must have six zeros.
Because we are given four zeros, f has two more zeros.
To find the remaining two zeros, recall the Complex Conjugate Root Theorem:
[tex]\displaystyle \text{If } a+bi \text{ is a zero, then } a-bi\text{ is also a zero.}[/tex]
Our two complex zeros are (2 + i) and (-3 - i).
Then by the above theorem, (2 - i) and (-3 + i) is the two remaining zeros of f.
