Quadratic Equation

Quadratic Equation

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.

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