- #1
Pietjuh
- 76
- 0
I've got to proof the following:
Let f be a monic polynomial in Q[X] with deg(f) = n different complex zeroes. Show that the sign of the discriminant of f is equal to (-1)^s, with 2s the number of non real zeroes of f.
I know the statement makes sense, because the discriminant is a symmetric polynomial over Q, so it can be written as a polynomial in elementary symmetric polynomials.
The question seems to suggest that the complex zeroes always come in pairs of a zero and its conjugate. But even if this is true, i still don't know how to proceed :(
Can anyone give me a hint?
Let f be a monic polynomial in Q[X] with deg(f) = n different complex zeroes. Show that the sign of the discriminant of f is equal to (-1)^s, with 2s the number of non real zeroes of f.
I know the statement makes sense, because the discriminant is a symmetric polynomial over Q, so it can be written as a polynomial in elementary symmetric polynomials.
The question seems to suggest that the complex zeroes always come in pairs of a zero and its conjugate. But even if this is true, i still don't know how to proceed :(
Can anyone give me a hint?