First of all: a polynomial of degree N has exactly N roots (in the complex plane) [ref]
Second: since for every root there is also its complex-conjugate [ref], we can only have some combinations...
Degree Roots Possible Combinations 1 1 Real Root 2 2 Real Roots, or 2 Complex Roots 3 3 Real Roots, or 1 Real and 2 Complex Roots 4 4 Real Roots, or 2 Real and 2 Complex Roots, or 4 Complex Roots etc etc!
Eventually, complex numbers are defined like this.
Saturday, November 05, 2011
Where (in the complex plane) are the solutions of an equation?
By at 17:25
Section: Personal, popular science
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