Fundamental Theorem of AlgebraDate: 01/25/2001 at 11:45:27 From: Nataria Joseph Subject: The Fundamental Theorem of Algebra What exactly is the Fundamental Theorem of Algebra? Date: 01/25/2001 at 11:58:49 From: Doctor Schwa Subject: Re: The Fundamental Theorem of Algebra The fundamental theorem of algebra says that any polynomial, ax^n + bx^(n-1) + ... with the a, b, etc. coefficients real or complex, can be factored completely into (x - r)(x - s) ... where the r, s, etc. are complex numbers. That is, every polynomial has solutions in the complex numbers. The interesting thing about that, to me, is that we are in some sense done inventing numbers once we get up to the complex. Equations like x + 5 = 2 make you invent negative numbers; equations like 2x = 3 make you invent fractions; equations like x^2 = 2 make you invent irrationals; equations like x^2 = -1 make you invent imaginaries; but even equations like x^2 = i can be solved just using more imaginary (complex) numbers. You don't need anything new! - Doctor Schwa, The Math Forum http://mathforum.org/dr.math/ |
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