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.

Posted Date: 4/8/2013 2:39:05 AM | Location : United States

Ask an Expert

Related Discussions:- Simple zeroes and multiplicity, Assignment Help, Ask Question on Simple zeroes and multiplicity, Get Answer, Expert's Help, Simple zeroes and multiplicity Discussions

Write discussion on Simple zeroes and multiplicity
Your posts are moderated

Write your message here..

Related Questions

Slope intercepts, (4, -5) , y = -1 (4, -5) , y = -1

Domain and range, Domain and Range The domain of any equation is the se... Domain and Range The domain of any equation is the set of all x's which we can plug in the equation & get back a real number for y. The range of any equation is the set of all

Crossword help, what is the three in four to the third power? what is the three in four to the third power?

Math, ab ab

Compound inequalities, -2 -2

#title.shawnee, 1/4 +2/3+4/24 show all work 1/4 +2/3+4/24 show all work

Ms. Pat, what is the simplified form of 5 square 32 - 4 square 18 what is the simplified form of 5 square 32 - 4 square 18

Equations with more than one variable, need help with solve a= 3p(4-2r) for... need help with solve a= 3p(4-2r) for p

Standard form of a quadratic, First, the standard form of a quadratic equat... First, the standard form of a quadratic equation is                                   ax2 + bx + c = 0                          a ≠ 0 Here the only needs are that we have an

Determine the two zeroes - factor theorem, Given that x=2 is a zero of P ( ... Given that x=2 is a zero of P ( x ) = x 3 + 2x 2 - 5x - 6 determine the other two zeroes. Solution Firstly, notice that we actually can say the other two since we know th