Editing Discriminant (section)

==Real roots==
In this section, all polynomials have [[real number|real]] coefficients.

It has been seen in {{slink||Low degrees}} that the sign of the discriminant provides useful information on the nature of the roots for polynomials of degree 2 and 3. For higher degrees, the information provided by the discriminant is less complete, but still useful. More precisely, for a polynomial of degree {{math|''n''}}, one has:
* The polynomial has a [[multiple root]] if and only if its discriminant is zero.
* If the discriminant is positive, the number of non-real roots is a multiple of 4. That is, there is a nonnegative integer {{math|''k'' ≤ ''n''/4}} such that there are {{math|2''k''}} pairs of [[complex conjugate]] roots and {{math|''n'' − 4''k''}} real roots.
* If the discriminant is negative, the number of non-real roots is not a multiple of 4. That is, there is a nonnegative integer {{math|''k'' ≤ (''n'' − 2)/4}} such that there are {{math|2''k'' + 1}} pairs of complex conjugate roots and {{math|''n'' − 4''k'' + 2}} real roots.