Quadratic Expression as a Perfect Square

Quadratic Expression as a Perfect Square

## Formula

$$ax^2+bx+c=(px+q)^2$$

requires:

$$a=p^2$$

$$b=2pq$$

$$c=q^2$$

Therefore, for a quadratic to be a perfect square:

$$b^2=4ac$$

## Conditions / Special Cases

This corresponds to:

$$D=0$$

Hence the quadratic has equal roots.

## Usage

- Used to identify perfect-square quadratics and simplify expressions.