JEE Mathematics B2A in Tamil | Season 0, Episode 3 | Fundamentals of Mathematics | Polynomial
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The document provides information about polynomials including: 1) The definition of a polynomial as an expression involving terms of various integer powers of x with the highest power term having a non-zero coefficient. 2) The remainder theorem which states that if a polynomial p(x) is divided by a binomial x-a, the remainder is equal to p(a). 3) The factor theorem which states that if a polynomial f(x) is equal to 0 at x=a, then (x-a) is a factor of the polynomial.
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To summarize the key steps for factoring polynomials:
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Let's analyze the remainder term R6 using the geometry series method:
|tj+1| = (j+1)π-2 ≤ π-2 = k|tj| for all j ≥ 6 (where 0 < k = π-2 < 1)
Then, |R6| ≤ t7(1 + k + k2 + k3 + ...)
= t7/(1-k)
= 7π-2/(1-π-2)
So the estimated upper bound of the truncation error |R6| is 7π-2/(1-π-2)
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This document is a math project submitted by Aman Yadav of class 9A on polynomials. It covers topics like the definition of polynomials, exponents and terms, degree of polynomials in one and two variables, the remainder theorem, factor theorem, and algebraic identities. It provides examples and questions to explain these concepts. Key points are defined like a polynomial being the sum of monomials, and the degree being the highest power of a variable in a polynomial.
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The document discusses sign charts of factorable polynomials and rational expressions. It defines a factorable polynomial as one that can be written as the product of real linear factors. An example polynomial is fully factored. Roots of the polynomial are defined as the values making each linear factor equal to zero. The order of a root is defined as the power of the corresponding factor. The Even/Odd-Order Sign Rule is stated: for a factorable polynomial, signs are the same on both sides of an even-ordered root and different on both sides of an odd-ordered root. An example sign chart is constructed applying this rule.
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- The degree of a polynomial is the exponent of its highest degree term. For example, in x^3 + 2x^2 + 4x + 5, the degree is 3.
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This document discusses various methods for finding the zeros or roots of polynomial functions, including factoring, factor theorem, synthetic division, and using the principle that every polynomial of degree n has n zeros. It provides examples of finding the zeros of polynomials by factorization, using a given zero to find other zeros through synthetic division, and identifying which numbers are zeros of various polynomials. Exercises are included for students to practice finding remaining zeros given one zero and identifying polynomial factors.
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Let's analyze the remainder term R6 using the geometry series method:
|tj+1| = (j+1)π-2 ≤ π-2 = k|tj| for all j ≥ 6 (where 0 < k = π-2 < 1)
Then, |R6| ≤ t7(1 + k + k2 + k3 + ...)
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= 7π-2/(1-π-2)
So the estimated upper bound of the truncation error |R6| is 7π-2/(1-π-2)
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1. The document discusses finding real roots of real polynomials. It provides examples of listing possible rational roots, factoring polynomials completely into real factors, and applying Descartes' Rule of Signs and the Theorem on Bounds to determine properties of roots.
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A polynomial is an expression involving variables and their powers, where the highest power is called the degree of the polynomial. Some key points:
- A polynomial consists of terms with variables raised to non-negative integer powers, plus coefficients which are constants.
- The degree of a polynomial is the power of the term with the highest exponent. For example, the degree of 3x4 + 2x2 is 4.
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Electricity - Resistors in series and parallel
Resistors in series and parallel.
For more other electricity chapters see our other files.
Electricity 10th standard science - physics.
Electricity
Electricity. Ohms law. and all other 10th standard physics concepts part 1.
see other parts for more information.
Current electricity Part -1
10th standard science chapter Tamil Nadu state board syllabus - chapter 12.
This is just a part 1 of current electricity chapter.
The next parts are available here, just check it out and learn Electricity.
Practical Learning and assessment
Advantages and disadvantages in practical learning method and practical assessment.
Why there is a practical learning in education?
B.Ed., course paper.
Role of ICT in examination
This document discusses the role of information and communication technology (ICT) in educational assessment. It states that ICT has led to changes in assessment by allowing for new formats like computer-based testing and higher-order learning outcomes. ICT can be used to support both formative and summative assessment. Examples of ICT tools for assessment include online testing platforms, survey tools, and software for creating and scoring tests. ICT also facilitates project-based assessment and helps support students with disabilities.
Details about CUCET entrance exam
CUCET entrance exam is for entering into Different central universities around India.
This ppt is specially based on CUTN (Central University of TamilNadu)
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LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
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significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
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to significant land degradation, adversely affecting the region's land cover.
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centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
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of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
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help of Advanced technologies like Remote Sensing and Geographic Information Systems is
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9
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Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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- 2. Polynomial • An expression of the form f(x) = a0xn+ a1xn-1 + a2xn-2 + ………… an-1x + an, where n is a non negative integer and a0, a1, a2,…………… an are real numbers and a0 ≠ 0 is called a polynomial. • Remainder Theorem + If a polynomial p(x) is divided by a binomial x-a, the remainder obtained is p(a). + Example: Find the remainder for p(x)=x3-4x2-7x+10 when divided with x-2. • Factor theorem + If f(a)=0 for a polynomial then (x-a) is a factor of the polynomial f(x). f(x)=(x-a) Q(x) + f(a)
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