Sign of a Quadratic

Sign of a Quadratic

## Formula

Let the roots of:

$$f(x)=ax^2+bx+c$$

be $$\alpha,\beta$$, with:

$$\alpha<\beta$$

Then:

### If $a>0$

$$f(x)>0\quad\text{for }x<\alpha\text{ or }x>\beta$$

$$f(x)<0\quad\text{for }\alpha<x<\beta$$

### If $a<0$

$$f(x)<0\quad\text{for }x<\alpha\text{ or }x>\beta$$

$$f(x)>0\quad\text{for }\alpha<x<\beta$$

At the roots:

$$f(\alpha)=f(\beta)=0$$

## Usage

- Used to solve quadratic inequalities and determine intervals where a quadratic is positive or negative.