Reciprocal Root Relations

Reciprocal Root Relations

## Formula

If $$\alpha,\beta$$ are roots of:

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

then:

$$\frac1\alpha+\frac1\beta=\frac{\alpha+\beta}{\alpha\beta}=-\frac bc$$

and:

$$\frac1{\alpha\beta}=\frac ac$$

provided:

$$c\ne0$$

## Usage

- Used to evaluate expressions involving reciprocal roots.