NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.2 Polynomials - PDF DownloadClass 10
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NCERT solutions for class 10 maths chapter 2 ex 2.2. Polynomials focus on the zeros of the linear polynomial, quadratic polynomial, cubic polynomial and their relations. While solving this exercise, the most important thing is to remember the formula given for the relation between the zeros.
NCERT solutions for chapter 2 ex 2.2 class 10 will teach you how to form polynomials when zeros are given. To solve this exercise, you need to revise the factorization method taught in previous classes. There are two questions in ex 2.2. Each question has six sub-divisions. The first question asks students to find the zeroes and to find a relationship between the zeroes and the coefficients. On the other hand, in question 2, students need to find quadratic numbers using sum and their product of zeroes.
eSaral offers a free PDF with NCERT solutions for ex 2.2 in class 10 maths. Class 10 maths chapter 2 exercise 2.2 NCERT solutions are presented in a step-by-step format. You will be able to solve these questions once you go through these solutions. you can download the PDF for better understanding of concepts.
Topics Covered in Exercise 2.2 Class 10 Mathematics Questions
It is advised that students thoroughly understand the topics covered by the ex 2.2. NCERT solutions for class 10 maths chapter 2 Polynomials ex 2.2 topics are mentioned below.
Relationship between Zeroes and Coefficients of a Polynomial
Relationship between Zeroes and Coefficients of a Polynomial - A polynomial is an expression with lots of different terms. Depending on the degree of polynomial, it can be divided into different types, like a linear polynomial (x), a quadratic polynomial (x2), or a cubic polynomial (x3). Based on the degree, we can easily find the zeros of any polynomial. A polynomial is a function whose coefficients are the constant values multiplied by its variables.
Here, you will learn the relationship between Zeroes and Coefficients of a Polynomial.
Linear Polynomial - Linear polynomials are generally defined as y = ax + b
We know that in the case of zeros, we have to find the point where y = 0. The general equation for y = 0 is:
y = ax + b
⇒0 = ax + b
x = -b/a
This tells us the relation between zero and the coefficient of the linear polynomial.
for a linear equation (y = ax + b, a ≠ 0), the graph of ax + b is a straight line that cuts the x-axis at (-b/a, 0)
Quadratic Polynomial - A Quadratic Polynomial is a degree of 2 polynomials. The zeroes of this polynomial can be determined using a variety of methods, including
Using Quadratic Formula.
Since Quadratic Polynomial has highest degree 2, There are two zeroes of the Quadratic Polynomial.
The relation between the zeroes of a quadratic polynomial and its coefficient is:
For any polynomial P(x) = ax2 + bx + c if the zeroes of the quadratic polynomial are α, and β then,
Sum of the zeroes (α + β) = – Coefficient of x / Coefficient of x2 = -b/a
Product of the zeroes (αβ) = Constant term / Coefficient of x2 = c/a
Cubic Polynomial - A cubic polynomial is a degree 3 polynomial, and because it has its highest degree of 3, there are three zeroes in a cubic.
Let’s suppose the zeros of the polynomials ax3 + bx2 + cx + d = 0 are p, q, and r, The relationship between these zeros and the polynomial and its coefficient will be given as follows:
Given Cubic Polynomials: ax3 + bx2 + cx + d = 0
If α, β, γ are the zeroes of the cubic polynomial ax3 + bx2 + cx + d, then
The sum of zeros, α + β + γ is -b/a = – Coefficient of x2/ coefficient of x3
The sum of the product of zeros, αβ+ βγ + αγ is c/a = Coefficient of x/Coefficient of x3
The product of zeros, αβγ is -d/a = – Constant term/Coefficient of x3
Tips for Solving Exercise 2.2 Class 10 Chapter 2 Polynomials
You can gain a thorough comprehension of the terms and concepts used in the questions of Ex 2.2 by following the tips given here.
Exercise 2.2 of NCERT solutions class 10 maths chapter 2 Polynomials may be solved by dividing the quadratic polynomial into multiple factors and writing each term separately. After separating the terms, you can take out the common factor and obtain the result. In this case, the remaining two terms can be considered to be factors.
Once students are familiar with polynomial degrees, how tosplit middle terms, and the relationship between the terms, they can easily solve the questions of ex 2.2 .
Importance of Solving Ex 2.2 Class 10 Maths Chapter 2 Polynomials
Here are some benefits of solving ex 2.2 class 10 maths chapter 2 polynomials.
NCERT solutions for exercise 2.2 chapter 2 of class 10 maths are relevant as it deals with questions from the fundamental form of equations.
If students are able to solve every question of this exercise 2.2 , they will understand the hit and try concept of finding the zeros of the polynomial and the concept of the discriminant as mentioned in chapter 2 exercise 2.2 of class 10 maths.
These NCERT solutions can help students to score high marks in their exams.
Frequently Asked Questions
Question 1. What is the formula for getting the sum of the roots of a polynomial ax²+ bx+ c = 0 ?
Answer 1. The formula for sum of roots = α + β = -(b/a). where b and a are the coefficients of the polynomial.
Question 2. Where can I find the best source for NCERT solutions for class 10 chapter 2 polynomial exercise 2.2 ?
Answer 2. You will find the best source for NCERT solutions for class 10 chapter 2 polynomial exercise 2.2 on the official website of eSaral. The NCERT solutions for Chapter 2 polynomials are created by subject experts in a stepwise manner according to the latest NCERT guidelines. These solutions will help you to understand the topic better and will also help you to revise for your exams.