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Wed 15 Dec, 2004 06:22 pm
Hello! What are the steps for finding the total amount of zeros (including rational, irrational, and complex) of a polynomial?
The "order" of the polynomial indicates the number of zeros. Keep in mind some can have a multiplicity of more than one. If you want to know how to find them, then that is another story.
Y0da wrote:The "order" of the polynomial indicates the number of zeros. Keep in mind some can have a multiplicity of more than one. If you want to know how to find them, then that is another story.
oh, i think i know how to find the zeros, but I don't know how to find the total amount without actually having to find all the zeros first. What's the "order"?
Order of Polynomials
The order is the highest power of "x" in the equation. So x^3+3=0 has an order of three and three solutions.
But in the case of an equation like xy^3, the order is actually four isn't it, because you add the exponenents and whichever is highest is the order. Is this right or am I just dreaming?
Multiple independent variables
When you have multiple independent variables, all bets are off. In the example you mentioned, xy^3=0, there are an infinite number of solutions of the form x=0, y=1,2,3,...
YOda is right.
The term with the highest power (this is the order or the degree of the equation or polynomial) indicates the number of solutions.
For example, a polynomial with a term having X^5 as its highest power has 5 solutions.
However, these solutions are gauranteed only in the set of COMPLEX numbers. That is, they may not all be real. Also, some may be solutions of multiplicity. That is, they occur more than once.