# Very strange about the zero degree polynomial

• Maisara-WD
In summary, the conversation discusses the form of a constant polynomial, where the value of 00 is often considered to be undefined but is conventionally given the value of 1 rather than 0. This convention is also used for power series and polynomials are still considered to be defined at 0. The conversation also mentions the existence of a hole on the y-axis when graphing a constant and how the y-intercept is excluded from the solution set.
Maisara-WD
Hi everybody

f(x) = aX0 is the form of any constant polynomial... right??
eg: f(x) = 3 is actually f(x) =3X0 where X belongs to R... ok??

since 00 is an unspecified quantity.. therefore on graphing a constant.. it should exists a hole on y-axis... and the y-intercept should not satisfy the function ie: excluded from the solution set. am I right.. HELP

00 was for a long time considered indeterminate or for some it was simply undefined. You have given one of a few reasons why 00 is conventionally given the value of 1 rather than 0 (there was much debate in the past over these two values specifically).

Even if 0^0 is considered undefined, polynomials are considered to be defined at 0. If you want to consider 0^0 undefined in general, then you will just have to get used to this convention. Also used for power series.

## What is a zero degree polynomial?

A zero degree polynomial, also known as a constant polynomial, is a polynomial expression in which all terms have a degree of zero. This means that the variable in the expression has no exponent or power, and the value of the polynomial remains constant regardless of the value of the variable.

## What is the degree of a zero degree polynomial?

The degree of a polynomial is the highest degree among all the terms in the expression. Since a zero degree polynomial has no terms with a degree higher than zero, the degree of a zero degree polynomial is zero.

## What is the graph of a zero degree polynomial?

The graph of a zero degree polynomial is a horizontal line that intersects the y-axis at a constant value. This is because the value of the polynomial remains the same for all values of the variable, resulting in a constant output.

## What are the roots of a zero degree polynomial?

The roots, or solutions, of a zero degree polynomial are the values of the variable that make the polynomial equal to zero. Since a zero degree polynomial has a constant value, it has no roots and cannot be solved for a specific value of the variable.

## What are some real-life applications of zero degree polynomials?

Zero degree polynomials are often used in economics and finance to represent constant values, such as fixed costs or constant interest rates. They can also be used in physics to represent the initial or final state of a system, where the value remains constant. Additionally, zero degree polynomials can be used as a basis for more complex polynomial expressions, making them an important concept in mathematics.

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