NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.4: Free NCERT Solutions for Class 10 Maths Chapter 2 X 2.4 PDF. Polynomials Class 10 Maths NCERT Solutions are extremely helpful while doing homework. Exercise 2.4 Class 10 Maths NCERT Solutions were prepared by experienced learnCBSE.in teachers. Detailed answers to all questions of Chapter 2 Maths Class 10 Polynomials Exercise 2.4 are given in the NCERT textbook.
NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.4
The NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Example 2.4 are part of the NCERT Solutions for Class 10 Maths. Here we have given Chapter 2 Polynomials Class 10 NCERT Solutions Example 2.4.
- Polynomials Class 10 Ex 2.1
- Polynomials Class 10 Ex 2.2
- Polynomials Class 10 Ex 2.3
- NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.4
| Board | CBSE |
| Textbook | NCERT |
| Class | Class 10 |
| Subject | Maths |
| Chapter | Chapter 2 |
| Chapter Name | Polynomials |
| Exercise | Ex 2.4 |
| Number of Questions Solved | 5 |
| Category | NCERT Solutions |
NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.4
Question 1.Verify that the numbers given below with cubic polynomials have their zeroes. Also, verify the relationship between the zeroes and the coefficients in each case:
On comparing the given polynomial with the polynomial ax3 + bx2 + cx + d, we obtain a = 2, b = 1, c = -5, d = 2
Thus, the relationship between the zeroes and the coefficients is verified.
On comparing the given polynomial with the polynomial ax3 + bx2 + cx + d, we obtain a = 1, b = -4, c = 5, d = -2.
Thus, the relationship between the zeroes and the coefficients is verified.
Concept insight: The zero of a polynomial is the value of the variable that makes the polynomial 0. Remember that there are three relationships between the zeroes of a cubic polynomial and its coefficients, which include the sum of zeroes, the product of all zeros, and the product. Two zeros were taken at once.
Question 2. Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, -7, -14 respectively.
Let the polynomial be ax3 + bx2 + cx + d and its zeroes be α, β, γ.
According to the given information:
If a = k, then b = -2k, c = -7k, d = 14k
Thus, the required cubic polynomial is k(x3 – 2x2 – 7x + 14), where k is any real number.
The simplest polynomial will be obtained by taking k = 1.
Concept insight: A cubic polynomial involves four unknowns and we have three relations associated with these unknowns, so the coefficients of a cubic polynomial can be found by assuming the value of one unknown and then finding the other three unknowns from the three relations.
Question 3. If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b.
Let p(x) = x3 – 3x2 + x + 1
The zeroes of the polynomial p(x) are given as a – b, a, a + b.
Comparing the given polynomial with dx3 + ex2 + fx + g, we can observe that
d = 1, e = -3, f = 1, g = 1
Therefore, the zeroes of p(x) are 1-b, 1, 1+b .
Concept Insight: When a polynomial and its zeroes are given, remember to apply the relation between zero and coefficient. These relations involve the sum of zeros, the product of zeros, and the product of two zeros at once.
Question 4. If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 ±√3, find other zeroes.
Therefore, x2 – 4x + 1 is a factor of the given polynomial. For finding the remaining zeroes of the given polynomial, we will carry out the division of
Hence, 7 and -5 are also zeroes of the given polynomial.
Concept insight: If a is zero of a polynomial p(x), where the power of p(x) is greater than 1, then (x – a) will be a factor of p(x), when p(x) (x – a), the remainder obtained will be 0 and the quotient will be a factor of p(x) using the division algorithm. Remember that if (x – a) and (x – b) are factors of a polynomial, then (x – a) (x – b) will also be a factor of that polynomial.
Question 5. If the polynomial x4 – 6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 – 2x + k, the remainder comes out to be x + a, find k and a.
By division algorithm,
Dividend = Divisor x Quotient + Remainder
Divisor x Quotient = Dividend – Remainder
It will be perfectly divisible by x2 – 2x + k.
10 – a – 8 x 5 + 25 = 0
10 – a – 40 + 25 = 0
– 5 – a = 0
a = -5
Thus, k = 5 and a = -5.
Conceptual Insight: When a polynomial is divided by any non-zero polynomial, it satisfies the division algorithm given below:
Dividend = Divisor x Quotient + Remainder
Divisor x Quotient = Dividend – Remainder
Hence, it can be said from this relation that the result (dividend-remainder) will be exactly divisible by the denominator.
We hope the NCERT Book Class 10 Maths Chapter 2 Polynomials Example 2.4 helps you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Example 2.4, comment below and we will get back to you at the earliest.*-
FAQ about NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.4
Q1: What is Exercise 2.4 in NCERT Class 10 Maths Chapter 2?
A1: Exercise 2.4 in NCERT Class 10 Maths Chapter 2, titled “Polynomials”, is a set of problems and exercises that focus on division of polynomials, including both long division and synthetic division methods.
Q2: Why is it important to study Exercise 2.4 of Chapter 2 in Class 10 Maths?
A2: Exercise 2.4 introduces the concept of polynomial division, a fundamental skill in algebra. It helps students understand how to divide one polynomial by another, which is essential for a variety of applications in math and science.
Q3: What topics are covered in Exercise 2.4 of Chapter 2 in Class 10 Maths?
A3: Exercise 2.4 primarily covers polynomial division, including both long division and synthetic division methods. You will learn how to divide one polynomial by another and find the quotient and remainder.
Q4: How can NCERT Solutions of Exercise 2.4 of Chapter 2 help students?
A4: NCERT Solutions for Exercise 2.4 provide step-by-step explanations and solutions to problems related to polynomial division. These solutions help students understand the division process, practice solving problems, and prepare effectively for exams.
Q5: Where can I find NCERT solutions for Class 10 Maths Chapter 2 Exercise 2.4?
A5: NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.4 can be found in a variety of sources including official NCERT textbooks, educational websites and online study platforms. You can also ask your teacher or tutor for guidance.
Question 6: Are NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.4 available for free?
A6: Many educational websites and platforms provide free access to NCERT Solutions for Class 10 Maths including Exercise 2.4. However, it is necessary to verify the credibility of the source to ensure the accuracy of the solutions.
Q7: How can I effectively use NCERT Solutions to prepare for my Class 10 Maths exam?
A7: To use NCERT Solutions effectively, start by reading the relevant chapter in your textbook. Then, use the solutions to practice solving the problems in Exercise 2.4. Pay close attention to the steps and explanations given in the solution to understand the division process completely.
Q8: Can I completely rely on the NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.4 for exam preparation?
A8: While NCERT Solutions are a valuable resource, it is recommended to supplement your studies with additional reference books, practice papers and guidance from teachers or tutors to have a comprehensive understanding of polynomial division and perform well in exams.
Q9: Are there any online platforms that provide video tutorials with NCERT solutions for Exercise 2.4 of Class 10 Maths Chapter 2?
A9: Yes, many online educational platforms provide video tutorials in addition to NCERT solutions. These video tutorials can provide visual explanations of polynomial division and enhance your understanding.
Question 10: How can I tackle the challenging polynomial division problems in Exercise 2.4?
A10: When faced with challenging problems, start by reviewing the division process and the steps involved. Practice similar problems and get help from your teacher or classmates if needed. It is important to understand the basics of polynomial division in order to tackle more complex problems.