Discriminant

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In algebra, the discriminant of a polynomial that is equal to zero with real or complex coefficients is a certain expression in these coefficients of the polynomial if and only if the polynomial has a multiple root (for example, a root with multiplicity greater than one) in the complex numbers.

For example, the discriminant of the quadratic polynomial

      is       .

If the discriminant is larger than zero, then there are two distinct real numbers.

If the discriminant is equal to zero, then there are two repeating real numbers, i.e. exactly one real number.

If the discriminant is smaller than zero, then there are two distinct complex numbers.