What is P and Q in a polynomial function?

The rational root theorem says, a rational zero of a polynomial is of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient .

What is the name for the quotient of two polynomials p and q where q is not zero?

Any rational expression can be written as the quotient of two polynomials P/Q with Q ≠ 0, although this representation isn't unique.

Is P and Q are two polynomials of degree 5 and 4?

It has been given that P and Q are two polynomials of degree 5 and 4 respectively. So, the highest exponent of P is 5 and that of Q is 4. When we subtract these two polynomials then the highest exponent of the resultant polynomial will also be 5. Therefore, the degree of p-q will be 5 .

Are sin and cos polynomials?

The trigonometric functions are periodic and cannot be described by a polynomial .

What is P by q formula?

Answer: In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q . For example, −3/7 is a rational number, as is every integer (e.g. 5 = 5/1).

You can calculate the p and q by using the total number of alleles of p or q divided by the total number of alleles in the population or finding q^2 to find q.

What is a 4 degree polynomial called?

A bi-quadratic polynomial . A polynomial of degree 4 is called bi-quadratic polynomial.

What are two polynomials with 4 or more terms?

[3xyz - 78p^2 + 11xy + 923y^5 - 56p + 41] and [89ab - 5abc + 13c^2 - 37a^3 + 21b] are two polynomials with four or more terms.

What are the 5 kinds of polynomial equation according to degree?

Types of Polynomials Based on its Degree Degree Polynomial Name Degree 1 Linear Polynomial Degree 2 Quadratic Polynomial Degree 3 Cubic Polynomial Degree 4 Quartic Polynomial 1 more row

What is the relationship between sine and cosine?

sin(x degrees) = cos(90 - x degrees) , and vice versa.

What is the sine and cosine rule?

The sine rule can be used to find an angle from 3 sides and an angle, or a side from 3 angles and a side. The cosine rule can find a side from 2 sides and the included angle, or an angle from 3 sides .

Are sin and cos always equal?

So the only point at which sine and cosine are equal is where interchanging the adjacent and opposite sides makes no difference - that is, when they're equal to each other, which happens only in the case of an isosceles triangle.

What does P mean in polynomials?

A polynomial is generally represented as P(x). The highest power of the variable of P(x) is known as its degree . Degree of a polynomial function is very important as it tells us about the behaviour of the function P(x) when x becomes very large. The domain of a polynomial function is entire real numbers (R).

What is P and q in quadratic functions?

'p' and 'q' represent the x-intercepts . The x-intercepts are the points where the graph crosses the x-axis.

What is P and q in a statement?

In conditional statements, "If p then q" is denoted symbolically by "p q"; p is called the hypothesis and q is called the conclusion . For instance, consider the two following statements: If Sally passes the exam, then she will get the job.

The (p,q)-sine and (p,q)-cosine polynomials and their associated(p,q)-polynomials (2024)

Abstract

The introduction of two-parameter $(p, q)$ -calculus and Lie algebras in 1991has spurred a wave of recent research into $(p, q)$ -special polynomials, including $(p, q)$ -Bernoulli, $(p, q)$ -Euler, $(p, q)$ -Genocchi and $(p, q)$ -Frobenius–Euler polynomials.These investigations have been carried out by numerous researchers in order to uncover a wide range of identities associated with these polynomials and applications. In this article, we aim to introduce $(p, q)$ -sine and $(p, q)$ -cosine based λ-array type polynomials and derive numerous properties of these polynomialssuch as $(p, q)$ -integral representations, $(p, q)$ -partial derivative formulae and $(p, q)$ -addition formulae.It is worth noting that the utilization of the $(p, q)$ -polynomials introduced in this study, along with other $(p, q)$ -polynomials, can lead to the derivation of various identities that differ from the ones presented here.

Keywords: Stirling number of second kind

MSC 2020: 05A30; 11B68; 11B73; 11B15; 11B83; 33D15

Funding statement: The third author Talha Usman would like to thank Scientific Research Department at University of Technology and Applied Sciences, Sur for supporting this work under Project No. UTAS-Sur-SRD-IRF 23-04/06.

References

[1] A. Belafhal, H. Benzehoua, A. Balhamri and T. Usman,An advanced method for evaluating Lommel integral and its application in marine environment,J. Comput. Appl. Math. 416 (2022), Paper No. 114600.10.1016/j.cam.2022.114600Search in Google Scholar

[2] A. Belafhal, H. Benzehoua and T. Usman,Certain integral transforms and their application to generate new Laser waves: Exton–Gaussian beams,Adv. Math. Models Appl. 6 (2021), no. 3, 206–217.Search in Google Scholar

[3] A. Belafhal, S. Chib, F. Khannous and T. Usman,Evaluation of integral transforms using special functions with applications to biological tissues,Comput. Appl. Math. 40 (2021), no. 4, Paper No. 156.10.1007/s40314-021-01542-2Search in Google Scholar

The (p,q)-sine and (p,q)-cosine polynomials and their associated (p,q)-polynomials (2024)

Abstract

References

FAQs

What is P and Q in a polynomial function? ›

What is the sine and cosine rule? ›

References

Degree	Polynomial Name
Degree 1	Linear Polynomial
Degree 2	Quadratic Polynomial
Degree 3	Cubic Polynomial
Degree 4	Quartic Polynomial