Polynomial Equation with Real Coefficients

Polynomial Equation with Real Coefficients

## Definition / Concept

For a polynomial with real coefficients, non-real roots occur in conjugate pairs.

## Formula

If:

$$P(z)=a_nz^n+a_{n-1}z^{n-1}+\cdots+a_1z+a_0$$

has real coefficients and:

$$P(z)=0$$

then:

$$P(\bar z)=0$$

Therefore, if $z$ is a non-real root:

$$\bar z\text{ is also a root}$$

## Usage

- Used to identify missing roots of polynomial equations with real coefficients.