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NCERT Exemplar Class 10 Maths Chapter 2 Solutions: Polynomials

NCERT Exemplar Class 10 Maths Solutions for Chapter 2 are prepared according to the CBSE class 10 exam guidelines. With the help of these exercises in NCERT Class 10 Maths Exemplar, you will learn about the polynomials of varying degrees such as linear, quadratic and cubic polynomials and the geometrical meaning of polynomials. You will also get to understand the relationship between the coefficients and zeroes of a polynomial and the division algorithm.

Chapter 2 of Class 10 Maths NCERT Exemplar contains 4 exercises consisting of 62 questions. There are short answer questions such as fill in the blanks or justification for statements that will enable you to understand the topics in depth. The exercises also consist of long answer questions that carry high weightage in the question paper. Solving the NCERT Exemplar Maths Class 10 exercises will help you to prepare for various exams of your level. 

We believe in providing you with answers that can be understood easily. Therefore, we have used simple student-friendly language in all the NCERT Exemplar solutions for the chapter. Also, you will find that the solutions at Instasolv are written in a step-by-step fashion to make the topics compatible with your conceptual understanding.

Important Topics in the NCERT Exemplar Class 10 Maths Solutions Chapter 2

Introduction

  1. If we consider p(x) as a polynomial, the highest power of the variable x will define the degree of the polynomial.
  2. For instance, a polynomial with the highest power as 1 of the variable is known as a linear polynomial.
  3. A polynomial with the highest power as 2 of the variable is known as a quadratic polynomial.
  4. A polynomial with the highest power as 3 of the variable is termed as a cubic polynomial.
  5. Again, considering p(x) as a polynomial and k as a real number, if we find the value of p(x) by replacing x by k, then p(x) at x=k is denoted as p(k).

Zeroes of a Polynomial

If in the above example, we obtain a real number such that p(k)= 0, then k is termed as the zero of the polynomial p(x).

Geometric Representation of Polynomials

  1. The graph of a linear polynomial is a straight line and this will intersect the x-axis at exactly one point.
  2. The graph of a quadratic equation will be either a downward or an upward-facing parabola depending on the coefficient of x2.
  3. We can also conclude that cubic polynomials can have a maximum of 3 zeroes.

Zeroes and Coefficients of a Polynomial

Consider a cubic polynomial ax3+bx2+cx+d with the zeroes as α,β and γ.

α+β=-b/a

αβ+βγ+γα=c/a

αβγ=-d/a

Division Algorithm for Polynomials

Given two polynomials as p(x) and g(x) such that g(x)≠0, it is possible to find the polynomials r(x) and q(x) such that,

p(x)=g(x)q(x)+r(x)

Where r(x)=0 or degree of r(x)< degree of g(x).

Exercise Discussion of the NCERT Exemplar Class 10 Maths Chapter 2

  1. Exercise 2.1 is objective in nature with a number of multiple-choice questions based on the graphical representation of quadratic polynomial and zeroes of polynomials.
  2. Exercise 2.2 consists of mainly conceptual short answer type questions such as you will be required to justify the mathematical statements or check if the given statements related to the relationship between zeroes and coefficients of polynomials are true or false.
  3. The third exercise 2.3 comprises of 10 questions with a variety of polynomials so that you become proficient in finding the zeroes of polynomials.
  4. Exercise 2.4 consists of long answer type questions of miscellaneous nature, where you will require comprehensive knowledge of the division algorithm, zeroes and their relationship with coefficients of polynomials in this chapter.
  5. Solving these exercises in NCERT Class 10 Exemplar thoroughly will help you stand out in other competitive exams of your level as well such as NTSE, olympiad, etc.
  6. You can get good marks in board exams by practising the exemplar exercises.

Why Use NCERT Exemplar Class 10 Maths Solutions Chapter 2 by Instasolv?

  1. The solutions to NCERT Exemplar Problems for Class 10 Maths Chapter 2 by experts at Instasolv are specially designed to help you with your homework and revision.
  2. These solutions at Instasolv will automatically enhance the efficiency of your self-study hours as some typical topics of the chapter like division of polynomials can be confusing without proper guidance. 
  3. Instasolv experts strictly comply with the CBSE guidelines and therefore, the answers prepared by them are very reliable.
  4. Instasolv solutions will clear all the basics of the chapter in an interactive manner.