# Thread: Remaining Zeros of f

1. ## Remaining Zeros of f

Information is given about a complex polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.

Degree = 3; zeros = 3 + 4i, 5

2. Originally Posted by magentarita
Information is given about a complex polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.

Degree = 3; zeros = 3 + 4i, 5
Since the polynomial is of degree three, it has 3 roots- you are already given 3: 5 and 3+ 4i. In order to have only real coefficients, the third root must be the complex conjugate of 3- 4i.

3. ## why....

Originally Posted by HallsofIvy
Since the polynomial is of degree three, it has 3 roots- you are already given 3: 5 and 3+ 4i. In order to have only real coefficients, the third root must be the complex conjugate of 3- 4i.
Why is the third root the complex conjugate of 3- 4i?