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Xam Idea Class 10 Maths Chapter 2 Solutions: Polynomials

Xam Idea Class 10 Maths Solutions for Chapter 2 ‘Polynomials’ are designed in a stepwise manner. With the questions given for exercises in Xam Idea Class 10 Maths Solutions Chapter 2, you will get to know about different concepts like the polynomials of varying degrees such as linear, quadratic and cubic polynomials and the geometrical meaning of polynomials. Also, you will learn about the coefficients and zeroes of a polynomial and the division algorithm.

Xam Idea Solutions for Class 10 Polynomials contain 6 exercises with an estimate of 63 questions in total. The exercises contain different types of questions like very short answer type questions, short answer type questions, long answer type questions, higher-order thinking questions and value-based questions. With the help of our solutions for Xam Idea Polynomials, you will learn how to find the total number of zeros in a case, the value of x given ‘a’ and ‘b’ as the zeroes of polynomial and how to verify relationships between the zeros and coefficients of a polynomial. Our solutions adhere to the latest guidelines laid down by CBSE and NCERT for Class 10 board exams.

The team of Instasolv offers you the right set of answers for Polynomials that are easy to understand. This is because the team of experts have efficiently used simple student-friendly language in all the Xam Idea Solutions to all the questions. Also, the solutions will help you in understanding the concepts in a step by step order in order to make the topics compatible with your understanding levels.

Important Topics For Xam Idea Class 10 Maths Solutions Chapter 2: Polynomials

 

Introduction

  1. In order to define the degree of a polynomial, you can consider p(x) as a polynomial that is the highest power of the variable x.
  2. A Linear polynomial is the one that has the highest power as 1 of the variable.
  3. A quadratic polynomial is the one that has the highest power as 2 of a particular variable.
  4. A cubic polynomial is the one that has the highest power of 3 of the variable.
  5. If you consider p(x) as a polynomial and k to be a real number, then if you would find the value of p(x) by replacing the x with k, then the value of the polynomial, p(x) at x=k will be denoted as p(k).

 

Zeroes of a Polynomial

Let us understand this with the help of an example,

If p(x) is replaced by p(k), and the real number obtained is p(k)=0, then the k term is known as the zero of a polynomial p(x).

 

Geometric Representation of Polynomials

  1. The output of a linear polynomial is a straight line graph that intersects the x-axis at one point.
  2. If you will draw the graph of any quadratic equation, you will get an output as a downward or upward-facing parabola that depends on the coefficient of x2.
  3. Also, you will know with the graphical representations that cubic polynomials contain a maximum of 3 zeroes.

Zeroes and Coefficients of a Polynomial

If you Consider a cubic polynomial ax3 + bx2 + cx + d with the zeroes as a ,ß, and ϒ, then the equations are:

Division Algorithm for Polynomials

Suppose, there are two types of polynomials, p(x) and g(x), such that, g(x) 0. 

It is then possible to find the values for polynomials r(x) and q(x) such that:

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

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

In the chapter, you will study all these topics in detail along with some descriptive examples that will help you ace the board exams.

Exercise Discussion of Xam Idea Class 10 Maths Chapter 2: Polynomials

Xam Idea Solutions Class 10 Maths Chapter 2 Polynomials includes 6 exercises. Here is a brief description of the exercises along with the types of questions included in them. 

Very Short Answer Type Questions

There are a total of 15 questions in this set of exercises where you need to find the number of zeroes in the given graphical figures, finding the relation between the degrees of polynomials p(x) and g(x), finding the type of equation given the zeros.

Short Answer Type Questions – I

This section contains a total of 10 questions where you will find the product of zeroes, finding the quadratic or any other type of polynomial given the sum and product of zeroes, or finding the value of k in a given polynomial.

Short answer type Questions-II

There are a total of 12 questions in this exercise set. The questions ask you to find the value of p in a question where the polynomial and remainders are given, finding the value of k given the zeroes of a polynomial, or verifying the relation between zeroes and coefficients.

Long Answer Type Questions

This set of exercise contains 6 questions in which you need to find zeroes given a type of polynomial say cubic polynomial, obtaining all the zeroes given two zeroes of a polynomial, finding the zeroes given the product of any two zeroes of a polynomial.

High Order Thinking Skills 

This set of exercise has only 3 questions that check your high order thinking skills in different types of questions. For example, you are given with two polynomials given the remainder after their division, and you need to find the values of k and α or any other variable given in the question, finding the inverse values of zeroes of a polynomial.

Value-Based Questions

The value-based questions are 17 in number that asks you to understand the question properly and eventually find the values depicted in the question. Also, you need to understand the value depicted by solving the questions that are based on different topics of the chapter.

Why Use Xam Idea Class 10 Maths Solutions Chapter 2: Polynomials by Instasolv?

  • The team of Instasolv makes combined efforts to provide the altered solutions to all the questions mentioned in Xam Idea Maths Chapter 2. 
  • Solving the Xam Idea Maths Class 10 questions will make the CBSE exam preparation easy for you. 
  • The solutions to the questions by Instasolv will enable you to understand all the topics in detail as the exercise section covers all type of questions. 
  • Our solutions are based on the guidelines of NCERT and CBSE.