Mathematics
The Fundamental Theorem of Algebra and Polynomial Factorization
Quick fact
The Fundamental Theorem of Algebra tells us that every polynomial equation of degree n has exactly n complex roots, counting multiplicities. This means that every polynomial can be completely factored into linear factors over the complex numbers, a fact first rigorously proved by Carl Friedrich Gauss in 1799.
Why this is interesting
You've learned that a quadratic equation always has two solutions—but did you know that this is just a special case of a much more powerful guarantee?