General Quadratic Root Relations

General Quadratic Root Relations

## Formula

For:

$$ax^2+bx+c=0$$

with roots $\alpha,\beta$:

$$\alpha+\beta=-\frac ba$$

$$\alpha\beta=\frac ca$$

If $\alpha,\beta$ are conjugates:

$$\alpha+\beta=2\operatorname{Re}(\alpha)$$

$$\alpha\beta=|\alpha|^2$$

## Usage

- Used to determine unknown coefficients or properties of complex roots without directly solving the equation.