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Mathematics LibreTexts

1.2: Fundamental Theorem of Algebra

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    6467
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    One of the reasons for using complex numbers is because allowing complex roots means every polynomial has exactly the expected number of roots. This is called the fundamental theorem of algebra.

    Theorem \(\PageIndex{1}\) Fundamental theorem of algebra

    A polynomial of degree \(n\) has exactly \(n\) complex roots (repeated roots are counted with multiplicity).

    In a few weeks, we will be able to prove this theorem as a remarkably simple consequence of one of our main theorems.

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