NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.4

NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.4 are created by askIITians experts to help you understand the Polynomials chapter effectively. You can download the stepwise solutions of this exercise for free and start practising at any time. Chapter 2 Polynomials of NCERT Class 10 Maths includes three main topics - zeros of a polynomial, the relationship between zeros and the coefficients of a polynomial and the division algorithm for polynomials. This exercise is based on miscellaneous questions related to these three main topics. By practising the questions of this exercise you will get a fair idea of how clearly you have understood the concepts of the chapter. Let us see why you must download the NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.4 from the askIITians website. 

About NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.4

The fourth exercise of NCERT Class 10 Maths Chapter 2 is an optional exercise. This means the questions given in this exercise are not from the examination perspective or will not be asked in the Class 10 Maths board examination. However, we recommend that you must solve this exercise to test whether you have understood all the main topics of the chapter or not. 

Important points regarding NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.4:

• Polynomial: A polynomial is a type of algebraic expression with variables, constants, and exponents combined using arithmetic operations like addition, subtraction and multiplication. 
• Degree of a Polynomial: The highest power of x in the polynomial p(x) is called its degree. For example, the degree of the polynomial 3x³ + 2x² + 4x + 10 = 0 is 3. 
  • Cubic Polynomial: A polynomial with degree 3 is called a linear polynomial. 
  • Quadratic Polynomial: A polynomial with degree 2 is called a linear polynomial. 
  • Linear Polynomial: A polynomial with degree 1 is called a linear polynomial. 
• Zeroes of a Polynomial: A real number c is known to be a zero of a polynomial p(x) if p(c) = 0. 
• Zeroes of a Linear Polynomial: The zero of linear polynomial p(x) = ax+b is -b/a or - Constant Term of p(x) / Coefficient of x 
• Zeroes of a Quadratic Polynomial: 
  • The general form of quadratic polynomial ax2 + bx +c where a ≠ 0 has two zeroes
  • Product of zeroes = c/a = Constant term/ Coefficient of x2.
  • Sum of zeroes = -b/a = - Coefficient of x/ Coefficient of x2.

 

• Zeroes of a cubic polynomial: 
  • The general form of a cubic polynomial ax3 + bx2 +cx + d where a ≠ 0 has three zeroes. 
  • Sum of zeroes = b/a = - Coefficient of x2/ Coefficient of x3.
  • Sum of the product of zeroes taken two at a time = c/a = Coefficient of x/ Coefficient of x3.
  • Product of zeroes = -d/a = - Constant term/ Coefficient of x3.
  • Division Algorithm of Polynomials: The division algorithm states that given any polynomial p(x) and any non-zero polynomial g(x), there are polynomials q(x) and r(x) such that:​
    p(x) = g(x) q(x) + r(x), 
    where r(x) = 0 or degree r(x) < degree g(x).

Let us now discuss the questions of NCERT Class 10 Maths Chapter 2 Polynomials Ex 2.4:

Ex 2.4 Q1: In this question, you are given some cubic polynomials and some numbers. You have to verify whether these numbers are zeroes of those cubic polynomials and if they are, you have to verify their relationship between the zeroes and the coefficients of the cubic polynomials. 

Ex 2.4 Q2: In this question, you are given the sum, sum of the product of zeroes taken two at a time, and the product of zeroes of a cubic polynomial. You have to find the corresponding cubic polynomial. This question is the exact opposite of the first question. Check how to solve it step by step using our NCERT free solutions for Class 10 Maths Chapter 2 Ex 2.4. 

Ex 2.4 Q3: In this question, you are given that zeroes of a cubic polynomial are a – b, a, a + b. You have to find the value of a and b. You can see that almost all questions of this exercise are based on cubic polynomials. You can solve the questions of this exercise only if you can solve the questions of the previous three exercises of the chapter. 

Ex 2.4 Q4: In this question, you are given a polynomial of degree 4 and two of its zeroes. You have to find the other two zeroes of the polynomial. It is a complex question. You can find its stepwise solution in our NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.4. 

Ex 2.4 Q5: In this question, you are given that a polynomial with degree 4 is divided by a polynomial with degree 2. You are also given its remainder and you have to find the missing values. It is an interesting question but a little tricky. Find its comprehensive solution in our NCERT Class 10 Maths Solutions for Chapter 2 Ex 2.4. 

Download NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.4 

Many students skip this exercise because it is an optional exercise and is not from the exam perspective. However, you must consider this exercise as a test of your knowledge and understanding of the chapter. You must solve every question of this exercise and solidify your understanding of the zeroes of a polynomial, the division algorithm of polynomials, and the relationship between zeroes of a polynomial and its coefficients. 

Features of NCERT Solutions for Class 10 Maths Chapter 2:

• The NCERT Solutions for Class 10 Maths are prepared carefully by askIITians experts to help you understand the chapter better. 
• These solutions are self-explanatory. You do not need any further guidance and can easily understand how to approach difficult questions as given in the fourth exercise of the Polynomials chapter. 
• You can download these NCERT Solutions for free and refer to them at any time you want. 
• These solutions will help solidify your conceptual understanding of the chapter and make it easier for you to tackle all kinds of questions in the exam. 

Download exercise-wise free NCERT Solutions for all exercises of Class 10 Maths Chapter 2 from the links given below: 

• NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.1
• NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.2
• NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.3
• NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.4

NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.4 FAQs

 

1. How many questions are there in NCERT Class 10 Maths Chapter 2 Exercise 2.4? 

NCERT Class 10 Maths Chapter 2 Ex 2.4 has 5 questions. This is an optional exercise that included advanced-level questions based on zeroes of a polynomial and the division algorithm of polynomials. 

2. Why download NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.4 from askIITians?

NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.4 are prepared by askIITians experts and include comprehensive solutions for every exercise question. You can download these solutions for free and refer to them whenever you want. 

3. Are there any other study materials for Class 10 Maths NCERT Chapter 2 Polynomials?

askIITians Maths experts have prepared free revision notes, sample papers, important questions, extra questions, mind maps, flashcards and practise worksheets for Class 10 Maths NCERT Chapter 2 Polynomials. You can download these solutions at any time. You can also enrol in our online CBSE Classes of Class 10 Maths and study in live, interactive sessions from your home.