Name given to the expression “B

^{2}– 4AC” that is used to find the solutions of the second-degree polynomial equation A*x*^{2}+ B*x*+ C = 0.### Symbol

The symbol “Δ”, read as “delta”, is generally used to represent the discriminant of a second-degree polynomial equation.

### Property

The sign of the discriminant provides information on the nature of the roots of the equation. The roots can be real and distinct if Δ > 0, real and equal if Δ = 0 or imaginary if Δ < 0.

### Examples

- Consider the equation
*x²*+ 5*x*– 12 = 0; the discriminant is Δ = 25 – 4(1 × –12) = 73. - Consider the equation 3
*x²*– 7*x*– 12 = 0; the discriminant is Δ = 49 – 4(3 × –12) = 193.