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 Ax² + Bx + 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.