A polynomial equation with rational coefficients has the roots 7 + sqroot of 3, 2 - sqroot of 6. Find two additional roots.
- 7 - sqroot of 3, 2 + sqroot of 6
- 3 - sqroot of 7, 6 + sqroot of 2
- 7 + sqroot of 3, 2 - sqroot of 6
- 3 + sqroot of 7, 6 - sqroot of 2
Based on the given roots, the additional roots can be found by taking the conjugates of the given roots.
Conjugate of 7 + √3 is 7 - √3
Conjugate of 2 - √6 is 2 + √6
Therefore, the two additional roots are:
- 7 - √3
- 2 + √6
So the correct answer is:
- 7 - √3, 2 + √6