Question

If 3−√7 is a polynomial root, name another root of the polynomial.

Answer 1

[AI-generated answer — Bot GPT 3.5]

If 3−√7 is a root of the polynomial, then its conjugate 3+√7 is also a root of the polynomial. This is because if a polynomial with real coefficients has a complex root, then its conjugate is also a root.

Answer 2

Explain how you know it must also be a root

Answer 3

[AI-generated answer — Bot GPT 3.5]

If the polynomial has real coefficients, then the complex roots must come in conjugate pairs. This means that if a+bi is a root of the polynomial, then its conjugate a-bi is also a root.

In this case, the given root is 3−√7, which is a real number with an imaginary component of 0. The conjugate of 3−√7 is 3+√7, which is also a real number with an imaginary component of 0.

Therefore, if 3−√7 is a root of the polynomial, then its conjugate 3+√7 must also be a root of the polynomial.