Question

`(5-√(5)) and (√(5) -5)`Are two roots of a fourth degree polynomial with integer coefficients, what are the other roots?

Answer 1

(5 +√5) and (-√5 -5)

Explanation:

Given two roots of the 4th-degree polynomial with integer coefficients are (5-√5) and (√5-5), you want to know the other two roots.

Conjugates

The other two roots are the conjugates of the given roots. That is, the signs of the √5 term will change:

(5 +√5) and (-√5 -5)

__

Additional comment

The polynomial is x⁴ -60x² +400.