information is given about a polynomial f(x) whose coefficients are real numbers. find the remaining zeros…
information is given about a polynomial f(x) whose coefficients are real numbers. find the remaining zeros of f. degree 3; zeros: 8, 6 - i the remaining zero(s) of f is(are) (use a comma to separate answers as needed.)
Answer
Explanation:
Step1: Recall conjugate root theorem
If a polynomial with real - number coefficients has a complex zero (a + bi), then its complex conjugate (a - bi) is also a zero of the polynomial.
Step2: Identify the given zeros
The given zeros are (8) (a real zero) and (6 - i) (a complex zero).
Step3: Find the remaining zero
Since the polynomial has real - number coefficients and (6 - i) is a zero, its complex conjugate (6 + i) must be a zero.
Answer:
(6 + i)