Transformed Roots: Reciprocal

Transformed Roots: Reciprocal

## Formula

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

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

then the roots:

$$\frac1\alpha,\frac1\beta$$

satisfy:

$$cx^2+bx+a=0$$

## Conditions / Special Cases

This transformation requires:

$$\alpha\ne0,\qquad\beta\ne0$$

which requires:

$$c\ne0$$

## Usage