Polynomial Factor from Conjugate Roots

Polynomial Factor from Conjugate Roots

## Formula

If:

$$\alpha=a+ib,\qquad\bar\alpha=a-ib$$

then:

$$(x-\alpha)(x-\bar\alpha)=(x-a)^2+b^2$$

Therefore:

$$x^2-2ax+(a^2+b^2)$$

is a real quadratic factor.

## Usage

- Used to construct real polynomial factors from conjugate complex roots.