University⏱ 4 min

Fundamental Theorem of Algebra

Every polynomial has n roots in ℂ

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r1r2

Polynomial

p(z)=z2−1p(z) = z²-1

Degree: 2 → 2 roots

deg⁡(p)=n⇒p exthasexactlyn extrootsinC\deg(p) = n \Rightarrow p \ ext{ has exactly } n \ ext{ roots in } \mathbb{C}

Fundamental theorem of algebra: every degree-n polynomial has exactly n roots in ℂ. The heat map shows |p(z)| – dark spots are roots (|p|≈0).