Question

A polynomial function, f(x), with rational coefficients has roots of -2 and irrational conjugates theorem states that which of the following must also be a root of the function?

a. -2i
b. 2i
c. 2
d. -2

Answer 1

The correct answer is -2i because it is the conjugate of -2, as per the irrational conjugate theorem.

Step-by-step explanation:

A polynomial function with rational coefficients and roots of -2 will have roots that are the conjugates of the irrational roots. Therefore, the correct answer is a. -2i because it is the conjugate of -2. The irrational conjugate theorem states that if a+bi is a root of the function, then a-bi must also be a root.