if a polynomial function f(x) has roots -8, 1, and 6i, what must also be a root of f(x)?\n-6\n-6i\n6 - i\n6
if a polynomial function f(x) has roots -8, 1, and 6i, what must also be a root of f(x)?\n-6\n-6i\n6 - i\n6
Answer
Answer:
B. $-6i$
Explanation:
Step1: Recall complex - conjugate root theorem
If a polynomial function with real - valued coefficients has a complex root (a + bi), then its complex conjugate (a - bi) is also a root of the polynomial.
Step2: Identify the complex root
Given roots are (-8), (1), and (6i). Since the polynomial has real coefficients and (6i=0 + 6i) is a complex root.
Step3: Find the conjugate
The complex conjugate of (6i) is (0-6i=-6i). So, (-6i) must also be a root of (f(x)).