Question

If 2+sqrt3 is a polynomial root, name another root of the polynomial, and explain how you know it must also be a root.

Answer 1

[AI-generated answer — Bot GPT 3.5]

Another root of the polynomial is 2-sqrt(3).

We know this must also be a root because if 2+sqrt(3) is a root of the polynomial, then the polynomial must be of the form (x - (2+sqrt(3)))(x - (2-sqrt(3))). When you multiply these two factors, you get a polynomial with the roots 2+sqrt(3) and 2-sqrt(3). Therefore, if one root is 2+sqrt(3), the other root must be 2-sqrt(3).

Answer 2

use simpler terms

Answer 3

[AI-generated answer — Bot GPT 3.5]

Sure! Another root of the polynomial is 2-sqrt(3). We know this must also be a root because when you have a polynomial with a root of 2+sqrt(3), the conjugate of that root (in this case, 2-sqrt(3)) must also be a root. This is because complex roots of a polynomial always come in pairs.