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The Fundamental Theorem of Algebra
You may already have noticed that quadratic equations always have a solution when including complex number solutions. It turns out this is true for any polynomial equation, of any degree! Learn about this and more, right here.
Sal introduces the Fundamental Theorem of Algebra, which, as is reflected in its name, is a very important theorem about polynomials.
The proof of the Fundamental Theorem of Algebra for any degree of polynomial is really tough. For now, let's note that it indeed holds for polynomials of the second degree (i.e. quadratics).
The Fundamental Theorem of Algebra can be used in order to determine how many real roots a given polynomial has. Check it out!