Simple zeroes and multiplicity, Algebra

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Now, we've got some terminology to get out of the way.

Multiplicity k

 If r is a zero of a polynomial and the exponent on the term that produced the root is k then we say that r has multiplicity k. 

Simple zeroes

Zeroes with a multiplicity of 1 are often called simple zeroes.

For instance, the polynomial P ( x ) = x2 -10x + 25 = ( x - 5)2  will have one zero, x= 5 , and its multiplicity is 2. In some of the way we can think of this zero as happening twice in the list of all zeroes as we could write the polynomial as,

                      P ( x ) = x2 -10x + 25 = ( x - 5) ( x - 5)

Written down this way the term x - 5 shows up twice and each term specified the same zero, x= 5 .Saying that the multiplicity of a zero is k is only shorthand to acknowledge that the zero will take place k times in the list of all zeroes.


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