The order of multiplicity is linked to the number of times a number is the root of a polynomial.
Before entering fully into the meaning of the term order of multiplicity , we are going to proceed to know the etymological origin of the two main words that give it shape:
– Order , first of all, derives from Latin. Specifically, it emanates from ordo, ordinis”, which can be translated as “order”.
– Multiplicity , secondly, comes from the Latin word multiplicitas , which is equivalent to “quality of having many ways.” It is a word that is the result of the sum of the following lexical components: the prefix multus- , which is synonymous with “many”; the verb plicare , which can be translated as “make folds”; and the suffix -dad , which is used to indicate “quality.”
Concepts related to the order of multiplicity
If we want to precisely define the idea of order of multiplicity , it is first necessary to review several terms from the field of mathematics . Otherwise, understanding the expression will be very complicated.
In this framework, it is worth referring to the concept of multiset . This is the name given to the set in which each member is linked to a multiplicity that indicates how many times the element in question is a member of the set .
In the multiset {a, a, a, a, b, c} , for example , the multiplicity of a is 4 , while the multiplicity of b and c is 1 .
On the other hand, it is important to keep in mind that polynomials are expressions formed by at least two algebraic terms that are joined by a minus sign ( – ) or a plus sign ( + ). Finally, the notion of root must be considered as the value that, in an equation, the unknown can have.
The root of a polynomial, then, is a number that allows the polynomial to be cancelled: when finding the numerical value, the result of the polynomial is 0 .
To calculate the order of multiplicity, the polynomial must be factored.
Polynomial factorization
Now we can move forward and focus on what the order of multiplicity is. This is the number of times a root is repeated in a polynomial . To determine it, it is necessary to factor the polynomial.
In other words , the order of multiplicity refers to how many times a certain number is the root of a polynomial . For example, if the root of a polynomial is 4 , the number of times that 4 appears as the root of said polynomial will be its order of multiplicity.
In the same way, it is necessary to know that the order of multiplicity becomes a very important element to be able to determine what the behavior of a polynomial function is with respect to what is called the "X" axis, which is also known as abscissa axis.
Other issues linked to the order of multiplicity
In addition to all of the above, there are another series of issues related to the order of multiplicity that are worth taking into account:
– If the aforementioned order of a root turns out to be even, the graph of the function in question touches the so-called “X” axis, but does not cross it. That is, it bounces.
– In the event that the order of multiplicity of a root is odd, the graph of that function crosses the aforementioned “X” axis, that is, it cuts it.