Question

Which of the following statements must be true about the polynomial function f(x)? If 1+ the sqrt of 13 is a root of f(x), then -1- the sqrt of 13 is also a root of f(x). If 1 + 13i is a root of f(x), then 1 – 13i is also a root of f(x). If 13 is a root of f(x), then –13 is also a root of f(x). If –13 + i is a root of f(x), then 13 + i is also a root of f(x).

Answer 1

Answer:

the correct answer is b on edge

Answer 2

The correct answer is: if $1 + 13i$ is a root of $f(x)$, then $1 - 13i$ is also a root of $f(x)$.

In fact, every polynomial has real and/or complex solutions. If all solutions are real, we're good. But if not all of them are real, then the complex ones come in couple of conjugate solutions. Since $1 + 13i$ and $1 - 13i$ are conjugate complex numbers, if one of them is a solution, the other must be as well.