If 3- squareroot 7 is root, name another root of the polynomial. explain how you know it must also be a root

Answer 1

To find another root of the polynomial, we need to consider the conjugate of the given root. The conjugate of 3-√7 is 3+√7.

To prove that 3+√7 is also a root, we substitute it into the polynomial and check if the resulting expression is equal to zero.

Let's substitute 3+√7 into the polynomial:
(3+√7)^2 - 7

Expanding the square:
(9 + 6√7 + 7) - 7
16 + 6√7 - 7
9 + 6√7

Since the result is equal to 9 + 6√7, which is not equal to zero, we can conclude that 3+√7 is not a root of the polynomial. Therefore, there is no other root of the polynomial based on the given root of 3-√7.