So yesterday, on math class, I solved a difficult task (a quadratic polynomial). I solved it correctly, but at one point teacher asked me something I couldn't explain. The task says: "The biggest value of the quadratic polynomial is 3/2 and one of his zeros is √3 - 1. Determine the polynomial if it's coefficients are rational numbers!". The first zero was √3 - 1, and I knew the other one had to be -√3 - 1 (I know it had to be it's conjugate). Teacher said that these are NOT complex numbers - so i cant conjugate anything. How can I prove that the rational coefficient [√3 - 1] is equal(?) to the rational coefficient [-√3 - 1]?