Learning how to solve quartic polynomials, which are polynomials in degrees of four in the form of f(x)=ax^4+bx^3+cx^2+dx+e, is not a very hard thing to do. It just takes a little time and dedication as well as knowledge about things such as end behavior, local extrema, zeros, Descartes rule of sign, intermediate value theorem, rational zero theorem, remainder theorem, remaining zeros and multiplicity and intercepts to understand the quartic polynomial even more. In this paper, all of
Georg Friedrich Bernhard Riemann was a revolutionary mathematician. He was born on September 17, 1826 in Breselenz, a village in Germany. His father, Friedrich Bernhard Riemann, who was a Lutheran minister, taught Riemann until he was ten. Then, Georg Friedrich Bernhard Riemann was taught by a teacher from a local school. Riemann had always displayed an interest in mathematics, especially when he studied at Lüneburg at the age of fourteen. His teacher gave him a textbook on a number theory by Legendre
The Fundamental Theorem of Algebra states that every polynomial equation of degree n, greater than or equal to one, has exactly n complex zeros. In fact, there are many equivalent formulations: for example that every real polynomial can be expressed as the product of real linear and real quadratic factors. The Fundamental Theorem of Algebra can also tell us when we have factored a polynomial completely but does not tell us how to factor a polynomial completely. Carl Friedrich Gauss was the first person
Evaluating Volterra Integro-Differential Equations in terms of Global, Polynomial and Numerical Equations in Boundary Conditions The integro-differential equations are originated from different mathematical models for many scientific phenomena. Nonlinear integro-differential equations are also can be seen in various applications of various scientific fields that are modeled by nonlinear phenomena.[3] The solutions using in integro-differential equations have an important role in lots of engineering
What Is Polynomial Regression A polynomial is a mathematical expression that is a sum of more than one monomial (Wikipedia). A monomial can be a constant, or a variable (also called indeterminate). In a monomial, the coefficients should be involved with only the operations of addition, subtraction, multiplication, and non-negative integer exponents (Wikipedia). For example, X2+5X-7 is a polynomial, and it is a quadratic one. Polynomial regression is the regression technique that tries to figure
Review of " On the irrationality of π4 and π6 " by Md. Reza Yegan INTRODUCTION "On the irrationality of π4 and π6 " by Md. Reza Yegan, taken from the Journal of Number Theory is a paper that, quite simply put, explores the concept of irrationality of 2 specific powers of π, namely π4 and π6. Referencing other papers as examples, Yegan states that, though the irrationality of π and π2 are often discussed, the irrational nature of the higher powers of π are usually neglected. Hence, Yegan chooses
Newton’s method is a tool used to find the roots of nearly any equation. Unlike the cubic and quadratic equations, Newton’s method – more accurately, the Newton-Raphson Method – can help to find roots of nearly any type of function, including all polynomial functions. Newton’s method use derivative calculus to find the roots of a function or relation by first taking an approximation and then improving the accuracy of that approximation until the root is found. The idea behind the method is as follows
Comprehensive Portfolio Project Alex Abel Table of Contents Title 1 Table of Contents 2 Matrices 3 Solving Systems of Equations 4 Solving Systems of Equations Cont. 5 Matrices Examples 6 Matrices Examples Cont. 7 Set Theory 8 Set Theory Examples 9 Equations 10 Equations 11 Equation Examples 12 Functions 13 Functions Cont. 14 Function Examples
are intersected by 2 lines, of varying slopes and shown the proof of its validity. I have used the TI-84 graphic display calculator, the software Geoegebra and Microsoft Excel to do my calculations. I have even investigated the values of D, for polynomials of higher powers and tried to come up with a general solution for all equations. I have been able to do this portfolio from the knowledge learnt from classroom discussions and through various other resources.
the vertex of the parabola being in the first quadrant and then change it so it holds true for the vertex is in any quadrant. Then I will prove my conjectures for other lines like y = 3x and 4x and so on and I will also change the degree of the polynomials and their values to prove the conjuncture to be true for values greater than 3. Using the dynamic graphing software GeoGebra construct the required graph Graphical solution for the given equation is given below (Fig 1.1)
Evariste Galois was a French boy born in Bourg-La-Reine October 25th 1811 to May 31st 1832. Born with both parents well educated in classical literature, religion and philosophy.There was never a record of mathematics in is family. Evaristes father was a republican who was head of the Bourg-la-Reine’s liberal party. When he was 10 his parents send him to a college in Reims where he got s grant. Soon his mother changed her mind thinking he would b defenseless on his own so she kept him home. His mother
Chapter Fourteen, Algebraic Thinking, Equations, and Functions, begins with defining the big ideas of algebraic and functional thinking. Each big idea is taught by combining objects and mathematical situations and the connection between the two. Algebraic and Functional thinking are taught as early as Kindergarten, where the teacher connects the mathematical situations to real world problems. Algebra is a broad concept; however, if we look at the number system, patterns, and the mathematical model
Calculus is defined as, "The branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two main types are differential calculus and integral calculus." (Oxford Dictionary). Contrary to any other type of math, calculus allowed Newton and other scientists to process the different motions and dynamic changes in world, such as the orbit of planets in space. Newton first became
Vocabulary Assignment #1 Nonexperimental Research (McMillan, 2012, p.13): Nonexperimental research is a quantitative research design in which the researcher has no control over any of the variables or factors within a study, and thus cannot influence the behavior of the subjects of the study. This phrase relates to a study that I may conduct because I would like to investigate how student-athletes’ academic achievement compares to that of non-student-athletes. In such an investigation, I would
Given the high anxiety level associated with the subject and the fact that so much of what we learn in algebra is not used by the general population, why is it so important that we teach it? Be honest! When was the last time you needed to factor a polynomial or to find the asymptotes in a rational expression. Unless you must use these ideas in your work, your answer is probably "huh?" Don't get me wrong, I think there are compelling reasons to teach algebra to the general population. The first reason
The problem of small oscillations can be solved through the study of molecular vibrations which further, can be introduced by considering the elementary dynamical principles. The solution for the problem of small oscillations can be found out classically, as it is much easier to find its solution in classical mechanics than that in quantum mechanics. One of the most powerful tools to simplify the treatment of molecular vibrations is by use of symmetry coordinates. Symmetry coordinates are the linear
Introduction to variables in statistics tutor: The variable which is available in the statistics it is called as statistical variable. It is a feature that may acquire choice in adding of one group of data to which a mathematical enumerates can be allocated. Some of the variables are altitude, period, quantity of profit, region or nation of birth, grades acquired at school and category of housing, etc,. Our statistics tutor defines the different types of statistics variables and the example of
One job the requires algebra is an Animator. Animators have to draw all kinds of pictures and cartoons and it requires them to use linear algebra for every movement a character or object may make. Algebra also helps create special effects to make the images shine and sparkle. The requirements you must have to do this type of job is that of course you have to have talent, some type of degree in animation, and be pretty decent in math. Animators make around $47,000 a year. Another job that requires
The Ljung-Box test is a test for serial correlation that tests if the autocorrelation coefficients for a given number of lags are jointly not significantly different from zero. The statistic for this test is where T is the sample size, m is the number of lags and is the estimated autocorrelation coefficient. The null hypothesis for this test is that the coefficients are all jointly zero and has a distribution. The alternative hypothesis is that at least one of the coefficients is not equal to
Algebra Requirement My personal view regarding algebra being a requirement for a degree program has changed from years pasted. If you had asked me this same question as a kid I would have said algebra as a requirement is a terrible idea. 7th grade was the first time I can remember ever seeing an algebra problem and to me it was like a foreign language. All the alphabets and numbers just didn’t make any since to me and many times I just except I wasn’t very smart in math. I struggled from that