Quadratic Equation and Complex Roots

Quadratic Equation and Complex Roots

## Formula

For:

$$ax^2+bx+c=0,\qquad a\ne0$$

the roots are:

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

The discriminant is:

$$D=b^2-4ac$$

## Conditions / Special Cases

If:

$$D>0$$

the roots are real and distinct.

If:

$$D=0$$

the roots are real and equal.

If:

$$D<0$$

the roots are non-real complex conjugates.

For $D<0$:

$$x=\frac{-b}{2a}\pm i\frac{\sqrt{-D}}{2a}$$

## Usage

- Used to classify and solve quadratic equations with real coefficients.