if 3- square root 7 is a polynomial root name another root of the polynomial. show your work

Question

explain how you know it must also be root.

Answer 1

To find another root of the polynomial, we can use the fact that if a is a root of a polynomial, then the conjugate of a is also a root.

Given that 3 - √7 is a root, its conjugate would be 3 + √7.

To show that 3 + √7 is also a root, we can substitute it into the polynomial and check if the polynomial evaluates to zero.

The polynomial is not given, so let's assume it is P(x).

Now substitute 3 + √7 into P(x):

P(3 + √7) = (3 + √7) - √7 = 3

Since P(3 + √7) = 3 ≠ 0, we can conclude that 3 + √7 is not a root of the polynomial.