Name given to the expression “B2 – 4AC” that is used to find the solutions of the second-degree polynomial equation Ax2 + Bx + 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 + 5x – 12 = 0; the discriminant is Δ = 25 – 4(1 × –12) = 73.
- Consider the equation 3x² – 7x – 12 = 0; the discriminant is Δ = 49 – 4(3 × –12) = 193.