Question

If 2 + √3 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]

To find another root of the polynomial, we can use the fact that if 2 + √3 is a root, then its conjugate, which is 2 - √3, must also be a root.

We know this because if a polynomial with real coefficients has a complex or irrational root, then its conjugate (the same number with the opposite sign in front of the irrational part) must also be a root. This property is a consequence of the conjugate root theorem.

In this case, since 2 + √3 is a root of the polynomial, by the conjugate root theorem, 2 - √3 must also be a root.