NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Exercise 2.4

The National Council of Educational Research and Training (NCERT) was founded in order to assist and advise the Central and State Governments on policies and programmes for the improvement of high-quality school education. It was established to enable and encourage the diverse cultural practises that are practised throughout the nation as a whole, as well as to support a unified educational system for the country with a national character. The basic goals of NCERT and its units are to conduct, promote, and coordinate research in school education-related disciplines. NCERT offers information about the globe and covers all significant topics. Students have moved away from the traditional approach to learning. It has precise content that students can readily understand. Additionally, it organises pre-service and in-service teacher training programmes, supports creative teaching methods, and collaborates and networks with other educational institutions, including NGOs and state education departments. The Central Board of Secondary Education advises students to use the NCERT textbooks. In addition to emphasising the benefits of learning from NCERT textbooks, CBSE claims that studying from NCERT can considerably improve students’ test performance.

Students struggle to decide which study material to use during examination preparation from the variety of options in front of them. Some of them frequently spend time looking for the best study materials in order to score high in their board examination. NCERT has taken on the responsibility of creating and spreading its own study materials in order to aid students in their exam preparations. These textbooks are incredibly helpful for CBSE students because they cover the whole CBSE curriculum and are primarily focused on helping the students prepare for their subsequent levels of education. To assist students with their studies, a team of experts created the NCERT series of books, which are thorough, knowledgeable, and well-written. When compared to other study tools, these NCERT books provide significant benefits to students in their board examination preparation.

These NCERT books are created by subject matter specialists after extensive research on a particular topic, which aids in laying a solid foundation for each subject. It also provides complete and in-depth information on the subject in clear and straightforward language. All of the significant concepts are included in the NCERT Mathematics solutions, along with detailed explanations for students’ understanding. The ideal framework for both board examinations and  other tests is provided by these NCERT study materials. Nearly all CBSE-affiliated schools advise their students to refer to NCERT books because they closely adhere to the CBSE curriculum and give students in-depth knowledge. The solutions provided by Extramarks contain crucial exam-related questions, solved sample papers from past years’ papers, solved sample papers, and much more. The NCERT books offer a wide range of examples with solutions, which aid students in comprehending ideas properly and enable themto adequately prepare for their CBSE board examinations. NCERT Solutions are given primary consideration by students when preparing for their board examinations. All of the exam-relevant questions are covered in NCERT textbooks, although they do not include detailed NCERT solutions.

The NCERT solutions are explained in a step-by-step manner in order to completely assist students in understanding the subject. The Extramarks website provides detailed NCERT Solutions to students to help them understand each topic clearly.Extramarks is an online learning platform that focuses on the pre-school, K-12, higher education, and test prep segments to enable learning anywhere, at any time, by combining education and technology.Interactive video modules on the Learning App ensure concept learning. These modules were created by a team of in-house subject matter experts who are highly skilled, providing 360-degree coverage of every concept and creating the opportunity for immersive online learning to promote greater comprehension and retention throughout examination preparation. The Assessment Centre, Smart Class Solutions, and Live Class Platform are just a few of the tools it provides to help students achieve their full potential through motivating instruction and individualised curriculum-based learning.

CBSE Class 10 NCERT Solutions for Maths Chapter 2 Polynomials Exercise 2.4

The NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 are offered to help students with their studies. These solutions are created by Extramarks’ subject specialists to help Class 10 board examination students study effectively. These experts produce the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 so that students can quickly and easily tackle the NCERT problems. They make sure that students can quickly learn from this and also pay attention to how easily they can understand the subject. It consists of additional chapter-related questions for practice. The NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4  present a series of questions, each with a detailed answer from the experts. Following NCERT criteria, the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 are created with the intention of covering the entire curriculum. These are highly beneficial for getting good examination results.

The Class 10th Math Exercise 2.4 is the fourth exercise in Class 10 Mathematics Chapter 2. In Class 9, Polynomials are introduced, but in Class 10, they are covered in greater detail. Students will be able to get additional marks after reading the detailed solutions provided by Extramarks subject-matter experts. It adheres to the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4, which aid in the students’ appropriate preparation. It contains all the crucial questions from the perspective of the examination.It helps students achieve high marks in mathematics board examinations. Students can complete and review all of the questions in the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 using these NCERT Solutions.

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Exercise 2.4

Mathematics is an important aspect of human logic and thought. It provides a powerful method for developing mental discipline and improvinglogical thinking. Additionally, understanding Mathematics is crucial in order to comprehend the concepts of other topics, like Science, Social Science, even Music and the Arts. Numerous professions and fields use Mathematics. Engineering, Science, and Economics questions are resolved using the principles and techniques of Mathematics. Mathematics is one of the most important subjects in a student’s academic career. If students wish to succeed in the subject, they must practise consistently. In order to perform well on their Class 10 board examinations, students should also have a strong understanding of mathematics because it is a conceptual subject.

Extramarks offers NCERT Solutions for Class 10 Maths, Chapter 2, Exercise 2.4. Polynomials are one of the most important topics in Class 10 Mathematics. It contains a comprehensive set of questions along with a summary. The NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 is an optional exercise, so it covers all topics and allows students to review the entire chapter. The NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 is designed to test students’ skills and cognitive thinking. It is used to see if a student can apply concepts learned throughout the chapter to complex problems in order to understand their progress. There are 5 problems in this section, each containing several sub-problems. With the help of this exercise, students will master the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 and Polynomial Topics, Polynomial Division Algorithms, and Polynomial Zeros.

Topics Covered

The NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 are detailed notes for Chapter 2 of the Mathematics textbook for Class 10 in the CBSE. Here, students will get an in-depth overview of Polynomials, including their types, algebraic expressions, degree, a graphical depiction of polynomial equations, factorization, the link between a polynomial’s zeros and coefficient, and more—all with an ample number of examples.

Extramarks provides the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4. This e-learning platform serves to show how technology may increase the effectiveness and simplicity of the learning process. The Extramarks website is committed to protecting the growth and prosperity of this community of students in order to enhance academic excellence. The practise of NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 is the first and most crucial phase in preparing for Mathematicssince it aids students in organising and developing their core concepts. If students practisethe solutions from the NCERT Textbook, they will be able to solve any complex problems that come up in their classroom, competitive exams, or board examinations with ease. To help them do better on examinations, students can discover reliable study materials such as NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 on the Extramarks website.

What is a Polynomial?

Students need to have a strong conceptual understanding of Mathematics, and if learning is done simply, it will be easier for students to understand the material. The Extramarks website is aware of the challenges and obstacles that many students confront, therefore, the teachers at Extramarks create the lesson plans and the course materials in a way that best meets their requirements. Class 10th Math Exercise 2.4 consists of important topics, so students should clearly understand every topic with the help of the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4.

A polynomial is an expression in Mathematics made up of coefficients and variables, commonly referred to as Indeterminates. It is a mathematical term for numerous terms since, as its name implies, “poly” means “many” and “nominal” means “phrases”. Typically, Polynomials are the product or difference of exponents and variables. Each term in the Polynomial is referred to as a “part.” Class 10 is considered a board class and students are under a lot of pressure to score high marks in their examinations. The Extramarks website helps them by providing them with the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4. With the help of the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 students can easily understand the concepts.

Types of Polynomial

Polynomials are grouped into three categories based on the number of terms they contain. There are three different kinds of polynomials that are, Monomial, Binomial, and Trinomial.

These polynomials can be combined using addition, subtraction, multiplication, and division, but never division by a variable.

An expression with only one term is called a monomial. The single term in an expression needs to be non-zero in order for it to be a monomial.

A polynomial expression with exactly two terms is referred to as a binomial. One way to think of a binomial is as the difference or sum of two or more monomials.

An expression with precisely three terms is called a trinomial.

What Are Zero Polynomials?

A Zero Polynomial is a kind of polynomial in which all the coefficients of the variables are equal to zero. In other words, it indicates that the powers of all the variables are equal to zero. A polynomial is an expression made up of variables and coefficients. The only polynomial with an uncertain degree is a zero polynomial. A polynomial’s degree is the highest degree of its non-zero terms; a polynomial with a value of zero has no non-zero terms. As a result, we cannot determine the degree of a polynomial using terms with degrees.

Exercise – 2.4

The NCERT Solutions Of Class 10 Maths Chapter 2 Exercise 2.4 are available on the Extramarks website to help students with their academics.  Extramarks subject matter experts created the NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.4 to assist students in their preparation for the Class 10 board examination.For students to quickly solve the NCERT questions, these specialists produce the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4. Along with ensuring that students can learn quickly from this, they also consider their ability to understand the NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.4.

Extramarks focuses on NCERT solutions, such as the  NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4, which are referred to by the CBSE, NCERT broadens the curriculum for students’ overall growth to include more than simply textbooks.

Students can practise the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 at Extramarks, a website that offers NCERT Solutions. Furthermore, Extramarks offers subject-matter experts, allowing students to ask them any questions they may have. Students are provided with worksheets from their teachers to assist them in identifying their areas of weakness, so they may improve on them and succeed in the examinations.

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Exercise 2.4 

The NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 provide a thorough understanding of Polynomials. This chapter will teach students about polynomials, their relevance, and their significance.Their comprehension of the idea of Polynomials will improve with the aid of the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4. To do well in mathematics, students must understand numerous key ideas in the Polynomials NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.4.Students can download the PDF of NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4. Additionally, they may get the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 to help students review the entire syllabus and do better on tests.

The formulas and techniques used in the NCERT Solutions for Class 10 Maths, Chapter 2, Exercise 2.4, can be difficult to grasp at times.With the help of the easily accessible NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 on Extramarks, students may revise at any time. Students must understand the steps and formulas required to complete the questions in this NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.4.The NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 might not be available to students on other websites. The learning and preparation processes can become more authentic if students choose the right study material. Students can rely on the Extramarks website to obtain the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4.

Clear the Concept First

Extramarks is a website that provides the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 so that students may comprehend all of the concepts. The top experts in India who are specialists in their professions are available to educate. The website has extensive media-based learning modules that go over every topic in great depth. Students’ grades and learning outcomes gradually increase as a result of their constant emphasis on concepts, detailed study, and speedy learning. The Extramarks’ website offers chapter-based worksheets, interactive activities, unlimited practise questions, and more in order to help students fully understand the concept. Students can check their knowledge with adaptive quizzes that have progressively harder difficulty levels, MCQs, and mock exams to form an upward learning graph.

Practice Problems

Extramarks provides the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 to assist students in preparing for and doing well in the CBSE Class 10 Maths examination.The  NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 is based on the board’s most recent syllabus. Students can prepare effectively for the board examination by practising the key questions for each chapter of the 10th standard Mathematics course. Students will get thorough answers. They can consult the solutions if they face trouble when attempting to answer   NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4.

The Extramarks website includes the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4, solved sample papers, past years’ papers, and other study materials. These resources are available to students who want to excel in their examinations. Students can learn independently and at their own speed with the Extramarks online learning platform. They can measure their success using AI-backed data and practise with individualised tests. To fully master all subjects and themes, Extramarks’ offers chapter-based worksheets, interactive activities, unlimited practise questions, and more.

Knowing About Polynomials Is Inevitable

Polynomials are an important aspect of Mathematics and Algebra “language.” They are used to express numbers that are the result of mathematical operations in almost every area of Mathematics. Other types of mathematical expressions, such as rational expressions, also use Polynomials as “building blocks.” Polynomials are used frequently by people. They are used by people to simulate a variety of structures and things, as well as in industries and construction. Even marketing, finance, and stocks employ them. The form of polynomial models is straightforward.

Polynomials are considered an important topic, and there are various aspects in the chapter. It is essential for students to fully comprehend the topic in order to understand it clearly. Therefore, the  NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 are provided by the Extramarks website to its students to help them in their preparation for the examination.

No Need to Put In Too Much Effort 

The NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 are available on the Extramarks website, where students may learn all the concepts. Additionally, Extramarks offers live doubt-solving sessions, so students can ask the teachers any query they may have. Teachers create worksheets for their students to assist them in identifying their areas of weakness so they may improve on them and perform well on the examination. The teachers at Extramarks tackle students’ queries that they are reluctant to ask their school teachers, thereby clearing their concepts.

The formulas and techniques used in the NCERT Solutions for Class 10 Maths, Chapter 2, Exercise 2.4, can be difficult to understand at timesWith the help of the easily accessible NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 on Extramarks, students may revise at any time. The steps and concepts required to finish the solutions to this problem must be understood by the students. Some websites may make it difficult for students to access the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 therefore by employing a dependable source, Extramarks, to obtain these answers, the learning and preparation processes can become more authentic. Students can rely on the Extramarks website to obtain NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4.

Facts

Polynomial equations are those created using exponents, coefficients, and variables.  The greater of its possible exponents is referred to as the degree of the polynomial. By factoring Polynomials according to their degree and the variables in the equation, students can find their solutions. The degree of a polynomial is determined by the highest degree monomial in the polynomial.Polynomials can be prime or factorable into products of primes, just like whole numbers. As long as each variable’s power is a nonnegative integer, they can include any number of variables. They serve as the foundation for solving algebraic equations.

Method of Division Polynomials

The step-by-step method of solving polynomial equations can be found on the Extramarks website and mobile application. Students can make use of these solutions to score well in their examinations.

Applications of Division Algorithm

An algorithm for dividing two integers, N and D, into their quotient and remainder, or the product of Euclidean division, is known as a Division Algorithm. Some are done manually, while software and digital circuit designs are used for others. Students can refer to the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 for help in clearly understanding the concept.

Why Extramarks?

The Extramarks website is an online website that provides NCERT Solutions for students who aim to score high marks in their examinations. NCERT Solutions Class 6, NCERT Solutions Class 7, NCERT Solutions Class 8, NCERT Solutions Class 9, NCERT Solutions Class 10, NCERT Solutions Class 11, and NCERT Solutions Class 12 are provided by the Extramarks to the students who are registered with its website to help them in keeping their concepts clear from the beginning itself.

Students are advised to study from the NCERT textbook solutions from Extramarks, like NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4, to prevent problems and queries related to the chapter. Extramarks is a simple solution for all students’ classes and subjects. Mathematics has never been easy for students, but with Extramarks guidance, they will find conceptualising Mathematics to be less challenging. When students’ practice and the guidance of Extramarks are combined, they will be able to achieve the best outcomes. For students to learn, practise, and succeed, the Extramarks website provides a variety of excellent educational courses.

Students may understand the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 with the use of the chapter-based worksheets, interactive exercises, an endless supply of practise problems, and other materials from Extramarks. On the Extramarks website, students can study at their own pace. By using Extramarks, students have access to sample papers and past years’ papers. It is possible to monitor each student’s readiness level. By establishing an account on Extramarks, students may get the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4. It offers detailed, published subject experts NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 offered by the Extramarks’ website.

The NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 guide students through the chapter summary. These solutions are organised by Extramarks’ expert educators and provided in step-by-step detail. As a result of these procedures, students may easily comprehend the chapter’s principles and the reasoning behind the questions. Students must fully comprehend the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 in order to build their foundational principles. They will be able to solve any challenging difficulties they come across throughout the examination with ease once they have practised these questions. Extramarks also provides young students with sample papers, previous years’ papers, revision notes, and significant questions for all subjects and classes, in addition to the NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.4.Sample papers and previous years’ papers are excellent resources for students studying for exams.Students can boost their confidence and do well on their board exams by practising sample papers and past years’ papers.

NCERT Solutions Class 10 Maths All Chapters

One of the most important subjects in a student’s academic career is Mathematics as it is a conceptual subject. If students wish to succeed in the subject, they must practise consistently. Students should also have a strong understanding of Mathematics in order to do well on their Class 10 board examination. NCERT Solutions for Class 10 Mathematics for all exercises from Chapters 1 to 15 are available on the Extramarks’ website. Extramarks’ knowledgeable faculty has selected these NCERT solutions to aid students in their test preparation. Students looking for the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 can download each PDF to find a more effective way to approach the problems.

The  NCERT solutions consist of all the chapter-by-chapter solutions to the questions found in the NCERT Book for Class 10 Maths, all of which have been prepared in a very exact and logical manner while upholding the goals of textbooks. As extra resources and study materials, the students may use the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4. Students’ examination preparation will undoubtedly benefit by practising the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4.

The NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 are designed to aid students in their exam preparation. All of the questions from the NCERT textbooks’ are included, along with NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4. In order to aid students in gaining a thorough understanding of the topics covered in Class 10, every NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 in the NCERT solution for Grade 10 is described in a practical and thorough manner. Since the majority of the questions in the NCERT are frequently asked in examinations, students can feel more confident that they will score well in their examinations. NCERT Solutions for Class 10 are designed to assist students in grasping the fundamentals of each topic, thereby enhancing their core knowledge.

NCERT Solutions Class 10 Maths Chapter 2 Exercises

Mathematics is an important subject for students in Class 10. The curriculum is structured so that students can learn new information and build a conceptual base before moving on to more complex topics. Extramarks’ NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.4 created by teachers would be of particular assistance with Class 10 Mathematical Chapter 2.Students may view the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 PDF file offline by downloading it.

Polynomials are the basis of Chapter 2 in Class 10 Mathematics. The various types of equations and their components are described in these NCERT Solutions for Class 10 Maths, Chapter 2, Exercise 2.4.Using the NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4 and finishing this chapter will make it simple for students to understand the concepts and handle the exercise questions. Students should refer to the NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.4 while practising the problems to quickly clear up any doubts.The Extramarks website offers NCERT solutions for all classes and courses.

Q.1

Verify that the numbers given alongside of the cubicpolynomials below are their zeroes. Also verify therelationship between the zeroes and the coefficientsin each case:(i) 2x3+x25x+2; 12,   1,   2(ii) x34x2+5x2; 2, 1, 1

Ans.

(i) 2x3+x25x+2; 12,   1,   2Let p(x)=2x3+x25x+2Thenp(12)=2(12)3+(12)25(12)+2            =14+1452+2=12+252=0p(1)=2(1)3+(1)25(1)+2            =2+15+2=0p(2)=2(2)3+(2)25(2)+2            =16+4+10+2=0Therefore, 12,   1 and  2 are zeroes of the given poynomial.Comparing the given poynomial with ax3+bx2+cx+d,we geta=2,  b=1,  c=5,  d=2Let the given roots are α,β and γ. Thenα = 12, β=1,  γ=2Now,α+β+γ=12+12=12=baαβ+βγ+γα=12×1+1×(2)+(2)×12=52=caαβγ=12×1×(2)=1=22=daThe relationship between roots and coefficients is verified.(ii) x34x2+5x2; 2, 1, 1Let p(x)=x34x2+5x2Thenp(2)=(2)34(2)2+5(2)2            =816+102=0p(1)=(1)34(1)2+5(1)2            =14+52=0Therefore, 2,   1 and  1 are zeroes of the given poynomial.Comparing the given poynomial with ax3+bx2+cx+d,we geta=1,  b=4,  c=5,  d=2Let the given roots are α,β and γ. Thenα = 2, β=1,  γ=1Now,α+β+γ=2+1+1=4=41=baαβ+βγ+γα=2×1+1×1+1×2=5=51=caαβγ=2×1×1=2=(2)1=daThe relationship between roots and coefficients is verified.

Q.2

Find a cubic polynomial with the sum of zeroes , sum of theproduct of its zeroes taken two at a time, and theproduct of its zeroes as 2, 7, 14 respectively.

Ans.

Let the polynomial be ax3+bx2+cx+d and its zeroes be α,  β and γ.Given thatα+β+γ=2=(2)1=baαβ+βγ+γα=7=71=caαβγ=14=141=daIf we take a=1,  b=2,  c=7 and d=14  then the required polynomial is x32x27x+14.

Q.3

If the zeroes of the polynomial x33x2+x+1are ab, a, a+b, find a and b.

Ans.

The given polynomial is x33x2+x+1  and its zeroesare ab, a, a+b.Sum of the roots = (ab)+a+(a+b)                                     =3a=Coefficient of x2Coefficient of x3=3a=1       Sum of the products of zero taken two at a time                       =a(ab)+a(a+b)+(a+b)(ab)                       =a2ab+a2+ab+a2b2                       =3a2b2=Coefficient of xCoefficient of x3=13a2b2=13.1b2=1b2=2b=±2Hence, a=1 and b=2  or 2

Q.4

If two zeroes of the polynomial x 4 6 x 3 26 x 2 +138x35 are2± 3 ,find other zeroes. MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8wrps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeqabeqadiWaceGabeqabeWaaqaafeaakq aabeqaaiaabMeacaqGMbGaaeiiaiaabshacaqG3bGaae4Baiaabcca caqG6bGaaeyzaiaabkhacaqGVbGaaeyzaiaabohacaqGGaGaae4Bai aabAgacaqGGaGaaeiDaiaabIgacaqGLbGaaeiiaiaabchacaqGVbGa aeiBaiaabMhacaqGUbGaae4Baiaab2gacaqGPbGaaeyyaiaabYgaca aMe8UaamiEamaaCaaaleqabaGaaGinaaaakiabgkHiTiaaiAdacaWG 4bWaaWbaaSqabeaacaaIZaaaaOGaeyOeI0IaaGOmaiaaiAdacaWG4b WaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaGymaiaaiodacaaI4aGa amiEaiabgkHiTiaaiodacaaI1aaabaGaaeyyaiaabkhacaqGLbGaaG jbVlaaikdacqGHXcqSdaGcaaqaaiaaiodaaSqabaGccaqGSaGaaGjb VlaabAgacaqGPbGaaeOBaiaabsgacaqGGaGaae4BaiaabshacaqGOb GaaeyzaiaabkhacaqGGaGaaeOEaiaabwgacaqGYbGaae4Baiaabwga caqGZbGaaeOlaaaaaa@80A2@

Ans.

Two zeroes of the polynomial x46x326x2+138x35are 2±3.Therefore, x2+3 and x23 are factors of thegiven polynomial.Now,x2+3x23=x23)x2+3)                                                               =x2232                                                               =x24x+43                                                               =x24x+1x24x+1 is also a factor of the given polynomial.Therefore, we divide x46x326x2+138x35by x24x+1 to find other factors.x24x+1x46x326x2+138x35                        x44x3       +x2                            +                                     2x327x2+138x352x3+8x2         2x+                      +¯                     35x2+140x35             35x2+140x35+                         +¯                           0                                 ¯x46x326x2+138x35                 =x24x+1x22x35                 =x2+3x23x27x+5x35                 =x2+3x23x7x+5x7andx+5arefactorsofx46x326x2+138x35.Hence,7and5arezeroesofx46x326x2+138x35.

Q.5

If the polynomial x46x3+16x225x+10 is dividedby another polynomial x22x+k, the remainder comesout to be x+a, find k and a.

Ans.

We know that​​​​​           Dividend = Divisor × Quotient + Remainderor DividendRemainder = Divisor × Quotientor (x46x3+16x225x+10)(x+a)=(x22x+k)×Quotientor x46x3+16x226x+10a=(x22x+k)×QuotientNow,x22x+kx24x+(8k)x46x3+16x226x+10a                                                         x42x3+      kx2    +                                                                ¯                              4x3+(16k)x226x+10a       4x3+    8x2             4kx       +                                 +¯                                         (8k)x2+(4k26)x+10a                   (8k)x2(2k+16)x+8kk2                   +                     +                                   +                 ¯                                           (2k10)x+k28k+10aRemainder  (2k10)x+k28k+10a must be zero.So,      (2k10)x+k28k+10a =02k10=0 or k28k+10a=0k=5 or 528×5+10a=0k=5 and a=5

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