Class 9 Exam > Class 9 Videos > Advance Learner Course: Mathematics (Maths) Class 9 > Relationship between Zeroes & Coefficient of Polynomials
Relationship between Zeroes & Coefficient of Polynomials Video Lecture | Advance Learner Course: Mathematics (Maths) Class 9
|
13 videos|79 docs|29 tests
|
FAQs on Relationship between Zeroes & Coefficient of Polynomials Video Lecture - Advance Learner Course: Mathematics (Maths) Class 9
| 1. What is the relationship between zeroes and the coefficient of polynomials? |  |
Ans. The relationship between the zeroes and the coefficient of polynomials is given by Vieta's formulas. For a polynomial of degree n, the sum of its zeroes is equal to the ratio of the coefficient of the second highest degree term to the coefficient of the highest degree term, multiplied by (-1) raised to the power of n. The product of the zeroes is equal to the ratio of the constant term to the coefficient of the highest degree term, multiplied by (-1) raised to the power of n.
| 2. How can the coefficient of a polynomial be determined from its zeroes? | |
Ans. To determine the coefficient of a polynomial from its zeroes, we can use Vieta's formulas. For a polynomial of degree n, the coefficient of the second highest degree term is equal to the sum of the product of the zeroes taken two at a time, multiplied by (-1). The constant term is equal to the product of all the zeroes, multiplied by (-1) raised to the power of n.
| 3. Can a polynomial have zeroes with different coefficients? | |
Ans. No, a polynomial cannot have zeroes with different coefficients. The zeroes of a polynomial are the values of the variable for which the polynomial equation becomes zero. Since the coefficient of each term in the polynomial determines its contribution to the value of the polynomial, the zeroes must satisfy the equation formed by equating the polynomial to zero. Therefore, all the zeroes of a polynomial have the same coefficient.
| 4. How can the coefficient of a polynomial affect its zeroes? | |
Ans. The coefficient of a polynomial can affect its zeroes in several ways. If a polynomial has a zero of multiplicity greater than 1, it means that the corresponding factor of the polynomial is repeated. This repetition is influenced by the coefficient of the polynomial. Additionally, the coefficient of the highest degree term in a polynomial can determine the overall behavior of the polynomial, such as whether it has a positive or negative leading coefficient, which in turn can affect the number and nature of its zeroes.
| 5. Can the coefficient of a polynomial be zero? | |
Ans. Yes, the coefficient of a polynomial can be zero. In a polynomial expression, each term consists of a coefficient multiplied by the variable raised to a certain power. If the coefficient of a term is zero, it means that the variable is absent from that term. This can happen when certain powers of the variable are missing from the polynomial expression. However, it's important to note that a polynomial is defined by having non-zero coefficients for at least one term.
About this Video
|
3.3K Views |
|
4.78/5 Rating |
|
Nov 22, 2024 Last updated |
Video Description: Relationship between Zeroes & Coefficient of Polynomials for Class 9 2024 is part of Advance Learner Course: Mathematics (Maths) Class 9 preparation.
The notes and questions for Relationship between Zeroes & Coefficient of Polynomials have been prepared according to the Class 9 exam syllabus.
Information about Relationship between Zeroes & Coefficient of Polynomials covers all important topics for Class 9 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Relationship between Zeroes & Coefficient of Polynomials.
Introduction of Relationship between Zeroes & Coefficient of Polynomials in English is available as part of our Advance Learner Course: Mathematics (Maths) Class 9 for Class 9 & Relationship between Zeroes & Coefficient of Polynomials in
Hindi for Advance Learner Course: Mathematics (Maths) Class 9 course. Download more important topics related with notes, lectures and mock test series for
Class 9 Exam by signing up for free.
Description
Video Lecture & Questions for Relationship between Zeroes & Coefficient of Polynomials Video Lecture | Advance Learner Course: Mathematics (Maths) Class 9 - Class 9 full syllabus preparation | Free video for Class 9 exam to prepare for Advance Learner Course: Mathematics (Maths) Class 9.
Information about Relationship between Zeroes & Coefficient of Polynomials
Here you can find the meaning of Relationship between Zeroes & Coefficient of Polynomials defined & explained in the simplest way possible.
Besides explaining types of Relationship between Zeroes & Coefficient of Polynomials theory, EduRev gives you an ample number of questions to practice Relationship between Zeroes & Coefficient of Polynomials tests,
examples and also practice Class 9 tests.
|
13 videos|79 docs|29 tests
|
|
Explore Courses for Class 9 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Free
,practice quizzes
,Previous Year Questions with Solutions
,Exam
,Objective type Questions
,Semester Notes
,study material
,Relationship between Zeroes & Coefficient of Polynomials Video Lecture | Advance Learner Course: Mathematics (Maths) Class 9
,Important questions
,ppt
,MCQs
,Sample Paper
,Summary
,video lectures
,Relationship between Zeroes & Coefficient of Polynomials Video Lecture | Advance Learner Course: Mathematics (Maths) Class 9
,past year papers
,shortcuts and tricks
,Viva Questions
,mock tests for examination
,Relationship between Zeroes & Coefficient of Polynomials Video Lecture | Advance Learner Course: Mathematics (Maths) Class 9
,Extra Questions
;
Study Relationship between Zeroes & Coefficient of Polynomials on the App
Students of Class 9 can study Relationship between Zeroes & Coefficient of Polynomials alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Relationship between Zeroes & Coefficient of Polynomials,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Relationship between Zeroes & Coefficient of Polynomials is prepared as per the latest Class 9 syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup