<p>Let&nbsp;\(P(z)\) be a polynomial with real coefficients. Then every complex (non-real) root of the equation \(P(z)=0\) occurs in conjugate pair, i.e., if&nbsp;\(\alpha \in \mathbb{C}\) is a root of the equation \(P(z)=0\), so is \(\alpha^*\).</p>

Let \(P(z)\) be a polynomial with real coefficients. Then every complex (non-real) root of the equation \(P(z)=0\) occurs in conjugate pair, i.e., if \(\alpha \in \mathbb{C}\) is a root of the equation \(P(z)=0\), so is \(\alpha^*\).

Applying the Conjugate Root Theorem

Complex Numbers

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Conjugate Pair-Roots Theorem

Conjugate Pair-Roots Theorem