Multiplicity of the zero, Algebra

Assignment Help:

The given fact will relate all of these ideas to the multiplicity of the zero.

Fact

If x = r is a zero of the polynomial P (x) along with multiplicity k then,

1.   If the value of k is odd then the x-intercept corresponding to x = r will cross the x-axis

2.   If value to k is even then the x-intercept corresponding to x = r will just touch the x-axis and not cross it actually.

Furthermore, if k = 1 then the graph will flatten out at the point x = r .

At last, notice that as we consider x get large in both the +ve or -ve sense (that means at either end of the graph) then the graph will either increase with no bound or decrease without bound. It will always occur with every polynomial and we can employ the following test to find out just what will happen at the endpoints of the graph.


Related Discussions:- Multiplicity of the zero

Vertex, All parabolas are vaguely "U" shaped & they will contain a highest ...

All parabolas are vaguely "U" shaped & they will contain a highest or lowest point which is called the vertex.  Parabolas might open up or down and may or may not contain x-inte

Relationship between the graph of a function and its inverse, There is inte...

There is interesting relationship among the graph of function and its inverse. Here is the graph of the function & inverse from the first examples. We'll not deal along with the

Word problem, Susan wants to mix 10 pounds of Virginia Peanuts that cost $...

Susan wants to mix 10 pounds of Virginia Peanuts that cost $3.50 a pound with Spanish peanuts that cost $3.00 a pound to obtain a mixture that cost $3.40 a pound. How many pounds

Writing linear equations, If you sell a kayak for $400 and your sales per d...

If you sell a kayak for $400 and your sales per day averages $5200. Assume the sales per day is a linear function of price of kayak. write an equation describing the relationship.

Pythagoras theorem.., find the perimeter of an irregulary shapep blocks of ...

find the perimeter of an irregulary shapep blocks of land didvided into 4 Triangles ab=12m by 15m bc =15m by 60m cd =24m by25m da = 25m by 48m..

Truth table-boolean expressions, 1. Construct a truth table for the followi...

1. Construct a truth table for the following Boolean expressions: a) ABC + A'B'C' b) ABC + AB'C' + A'B'C' c) A (BC' + B'C) 2.   Simplify the following expressions:

Use synthetic division to divide equation, Use synthetic division to divide...

Use synthetic division to divide 5x 3 - x 2 + 6 by x - 4 . Solution Okay along with synthetic division we pretty much avoid all the x's and just work with the numbers in

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd