If 2 + squareroot 3 is a polynomial root, name another root of the polynomial and explain how you know it must be a root.

Solution:

Given, 2 + squareroot 3 is a polynomial root.

We have to find another root of the polynomial.

The solution of the polynomial can be found by using the quadratic formula,

x = -b ± √(b² - 4ac) / 2a

This implies the roots are [ -b + √(b² - 4ac) / 2a] and [ -b - √(b² - 4ac) / 2a].

2 + squareroot 3 can be written as 2 + √3.

Using the quadratic formula,

Another root = 2 - √3

We can also say that complex roots always come with conjugate pairs.

Therefore, the required root is 2 - √3.

If 2 + squareroot 3 is a polynomial root, name another root of the polynomial and explain how you know it must be a root.

Summary:

If 2 + squareroot 3 is a polynomial root, another root of the polynomial is 2 - √3.