Expression often used as a synonym for a

*second-degree*polynomial equation.### Properties

A second-degree equation has 0, 1 or 2 roots.

The general form of a second-degree polynomial equation is A*x*² + B*x* + C = 0.

The value of the discriminant is ∆ = B² – 4AC.

- If ∆ > 0, the two roots are real and different.
- If ∆ = 0, the two roots are real and equal.
- If ∆ < 0, the two roots are imaginary and conjugate.
- If Δ ≥ 0, the roots are real and : \(x_{1}\) = \(\frac{-B + \sqrt{{B}^{2} − 4AC}}{2A}\) et \(x_{2}\) = \(\frac{−B − \sqrt{{B}^{2} − 4AC}}{2A}\).

### Educational note

- It is preferable to replace the expression
*quadratic equation*by*second-degree polynomial equation*. - The term “quadratic” concerns specific mathematical forms.