Question

Using the given zero, find one other zero of f(x). Explain the process you used to find your solution.

Answer 1

Complex zeroes always occurs as conjugates.
For z = a + b i conjugate is: a - b i
Another zero is : 2 + 3 i.
Verification:
2 + 3 i + 3 - 3 i = - b/a
- b = 4,  a = 1
( 2 + 3 i ) ( 2 - 3 i ) = c / a
4 - 9 i² = c / a
4 + 9 = c / a
c = 13
( x^4 - 4 x³ + 14 x² - 4 x + 13 ) : ( x² - 4 x + 13 ) = x² + 1
x² + 1 = 0
x² = -1,  x = i,  x = -i
The zeroes are: - i , i , 2 + 3 i, 2 - 3 i.
Answer: 
One another zero of f ( x ) is 2 + 3 i.