Question

if you know that 3+sqrt 11 is a root of a polynomial function, then the name given to 3 -sqrt 11, another root of that same function, is a______conjugate?

Answer 1

Answer: Radical conjugate.

Step-by-step explanation:

By definition  $a+\sqrt{b}$ and $a-\sqrt{b}$ are called "Conjugate radicals".

Therefore, by this definition, you can know the following:

1) $a+\sqrt{b}$ is the conjugate of $a-\sqrt{b}$

2) $a-\sqrt{b}$ is the conjugate of $a+\sqrt{b}$.

Then, since you know that $3+\sqrt{11}$ is a root of a polynomial function, therefore you can conclude that the name given to the other root $3-\sqrt{11}$ of the same function is the following:

"Radical conjugate".