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NCERT Revised Solutions for Class 10 Maths Chapter 4 Quadratic Equations in English and Hindi Medium for CBSE Board Exams. NCERT Class 10 Mathematics textbooks are based on NCERT Math books published for Session 2024-25. NCERT Book Solutions for Class 10 Maths Chapter 4 Quadratic Equations are essential for students aiming to master this crucial topic. Quadratic equations form the foundation for many advanced mathematical concepts, making it important for students to understand them thoroughly. NCERT 10th Math solutions provide step-by-step guidance to tackle complex problems, ensuring a clear understanding of concepts. The Quadratic Equations Class 10 NCERT Textbook Solutions focus on various methods, such as factorization, completing the square and using the quadratic formula. Available in easily accessible formats like NCERT Exercises Class 10 Maths Chapter 4 PDF, these solutions cater to diverse learning preferences.
Class 10 Maths Chapter 4 NCERT Textbook Solutions for CBSE
Class 10 Maths Chapter 4 Exercise 4.1
Class 10 Maths Chapter 4 Exercise 4.2
Class 10 Maths Chapter 4 Exercise 4.3
Class 10 Maths Chapter 4 Important Questions
Class 10 Maths Chapter 4 Solutions for State Boards
With detailed explanations and illustrations, students can grasp the logic behind solving quadratic equations effectively. By referring to CBSE Class 10 Maths Chapter 4 NCERT Exercises Solutions PDF, students can practice and review concepts repeatedly, enhancing their problem-solving skills and building confidence for exams.
Class 10 Maths Exercise 4.1
Class 10 Maths Exercise 4.2
Class 10 Maths Exercise 4.3
Class 10 Maths Exercise 4.4
The Quadratic Equations NCERT Exercises Solutions Class 10 offer a comprehensive approach to understanding this chapter’s various exercises. CBSE Class 10 Mathematics Quadratic Equations NCERT Textbook Solutions delve into real-life applications, helping students relate theoretical concepts to practical scenarios. NCERT 10th Math solutions simplify complex questions and ensure students gain clarity in solving equations systematically. Whether it’s learning to determine the roots of an equation or analyzing the nature of roots, the NCERT Detailed Solutions Chapter 4 Class 10 Maths are invaluable resources.
NCERT Mathematics Chapter 4 Exercise Solutions PDF provides a convenient way for students to study on-the-go, catering to the needs of tech-savvy learners. Quadratic Equations NCERT Math Chapter 4 Class 10 explains critical concepts with examples, ensuring students are well-prepared for board exams. Students can also use NCERT Grade 10 Maths Chapter 4 Complete Solutions for revision and quick recaps, saving time during exam preparations.
Key Points for Class 10 Maths Chapter 4 Quadratic Equations in Board Exams
Class 10 Maths Chapter 4, Quadratic Equations, focuses on solving equations using factorization, completing the square and the quadratic formula. Key topics include finding roots, analyzing the nature of roots (real and imaginary) and practical applications. Understanding formulas, step-by-step methods and real-world problem-solving is essential for board exam success.
| Day | Topics | Practice |
|---|---|---|
| Day 1 | Introduction to Quadratic Equations | Examples 1-5 from NCERT |
| Day 2 | Solving by Factorization | Exercise 4.2 (Questions 1-5) |
| Day 3 | Completing the Square Method | Examples 6-8, Exercise 4.3 (Questions 1-4) |
| Day 4 | Quadratic Formula | Examples 9-10, Exercise 4.4 (Questions 1-3) |
For those looking to excel in board exams, the NCERT Textbook Solutions for Class 10 Mathematics Quadratic Equations are an indispensable study tool. These solutions break down the complexities of Quadratic Equations Class 10 Math NCERT Exercise Solutions into digestible parts, enabling students to develop a strong conceptual understanding. NCERT Detailed Solutions for Class 10 Maths Chapter 4 include worked-out examples, detailed explanations and additional practice questions to ensure thorough preparation. By using the CBSE Class 10 Mathematics Chapter 4 NCERT Solutions PDF, students can focus on solving problems efficiently and understanding the underlying principles.
The Quadratic Equations Solutions for Class 10 Math emphasize both theoretical and application-based learning, ensuring students are exam-ready. With regular practice and a clear understanding of Quadratic Equations NCERT Solutions Class 10, students can significantly improve their problem-solving speed and accuracy, achieving excellent results in mathematics.
| Class: 10 | Maths |
| Chaper 4: | Quadratic Equations |
| Content: | Exercise and Extra Questions |
| Content Mode: | Text, Images, PDF and Videos |
| Academic Session: | Year 2024-25 |
| Medium: | English and Hindi Medium |
Simplified NCERT Solutions for class 10 Maths Chapter 4
The Hindi Medium solutions for the academic session 2024-25 for class 10 Maths chapter 4 are given here. These solutions are helpful for UP Board students studying in Class 10. 10th Maths Chapter 4 solutions are online for study or download in PDF format.
Download Assignments for practice with Solutions
10th Maths Chapter 4 Assignment 1
10th Maths Chapter 4 Assignment 2
10th Maths Chapter 4 Assignment 3
10th Maths Chapter 4 Assignment 4
10th Maths Chapter 4 NCERT Solutions follows the current CBSE syllabus. Students of MP, UP, Gujarat board and CBSE can use it for Board exams. Class 10 Maths NCERT Solutions Offline Apps in Hindi or English for offline use. For any scholarly help, contact us. We will try to help you in the best possible ways.
10th Maths Chapter 4 Solutions
Textbook Solutions for class 10 Maths Chapter 4 are given below in PDF format or view online. Solutions are in Hindi and English Medium. Uttar Pradesh students also can download UP Board Solutions for Class 10 Maths Chapter 4 here in Hindi Medium.
Learning quadratic equations is very important because they have many uses in various fields. Not only are they applied in other areas of mathematics and physics, but they are also useful in real-life situations. Understanding quadratic equations helps in solving many practical problems. You can download the NCERT books for the 2024-25 session, as well as revision materials and solutions, from the links provided here.
Previous Year’s CBSE Questions
1. Two marks questions
Find the roots of the quadratic equation √2 x² + 7x + 5√2 = 0. [CBSE 2017] 2. Find the value of k for which the equation x²+k(2x + k – 1) + 2 = 0 has real and equal roots. [CBSE 2017]
2. Three marks questions
If the equation (1 + m² ) x² +2mcx + c² – a² = 0 has equal roots then show that c² = a² (1 + m²).
3. Four marks questions
Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream. [CBSE 2017]
HISTORICAL FACTS!
The word quadratic is derived from the Latin word “Quadratum” which means “A square figure”.
Brahmagupta (an ancient Indian Mathematician)(A.D. 598-665) gave an explicit formula to solve a quadratic equation. Later Sridharacharya (A.D. 1025) derived a formula, now known as the quadratic formula, for solving a quadratic equation by the method of completing the square. An Arab mathematician Al-khwarizni(about A.D. 800) also studied quadratic equations of different types. It is believed that Babylonians were the first to solve quadratic equations. Greek mathematician Euclid developed a geometrical approach for finding lengths, which are nothing but solutions of quadratic equations.
Important Questions on Class 10 Maths Chapter 4
Check whether the following is quadratic equation: (x + 1)² = 2(x – 3)
(x + 1)² = 2(x – 3)
Simplifying the given equation, we get (x + 1)² = 2(x – 3)
⇒ x² + 2x + 1 = 2x – 6
⇒ x² + 7 = 0 or x² + 0x + 7 = 0
This is an equation of type ax² + bx + c = 0.
Hence, the given equation is a quadratic equation.
Represent the following situation in the form of quadratic equation: The product of two consecutive positive integers is 306. We need to find the integers.
Let the first integer = x
Therefore, the second integer = x + 1
Hence, the product = x(x + 1)
According to questions,
x(x + 1) = 306
⇒ x² + x = 306
⇒ x² + x – 306 = 0
Hence, the two consecutive integers satisfies the quadratic equation x² + x – 306 = 0.
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
Let, Shefali’s marks in Mathematics = x
Therefore, Shefali’s marks in English = 30 – x
If she got 2 marks more in Mathematics and 3 marks less in English,
Marks in Mathematics = x + 2
Marks in English = 30 – x – 3
According to questions,
Product = (x + 2)(27 – x) = 210
⇒ 27x – x² + 54 – 2x = 210
⇒(-x)² + 25x – 156 = 0
⇒ x² – 25x + 156 = 0
⇒ x² – 12x – 13x + 156 = 0
⇒ x(x – 12) – 13(x – 12) = 0
⇒ (x – 12)(x – 13) = 0
⇒ (x – 12) = 0 or (x – 13) = 0
Either x = 12 or x = 13
If x = 12 then, marks in Maths = 12 and marks in English = 30 – 12 = 18
If x = 13 then, marks in Maths = 13 and marks in English = 30 – 13 = 1
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
Let the larger number = x
Let the smaller number = y
Therefore, y² = 8x
According to question,
x² – y² = 180
⇒ x² – 8x = 180 [As y² = 8x]
⇒ x² – 8x – 180 = 0
⇒ x² – 18x + 10x – 180 = 0
⇒ x(x – 18) + 10(x – 18) = 0
⇒ (x – 18)(x + 10) = 0
⇒ (x – 18) = 0 or (x + 10) = 0
Either x = 18 or x = -10
But x ≠ -10 , as x is the larger of two numbers.
So, x = 18 Therefore, the larger number = 18
Hence, the smaller number = y = √144 = 12
Sum of the areas of two squares is 468 m². If the difference of their perimeters is 24 m, find the sides of the two squares.
Let the side of larger square = x m
Let the side of smaller square = y m
According to question,
x² + y² = 468 …(i)
Difference between perimeters,
4x – 4y = 24
⇒ x – y = 6
⇒ x = 6 + y … (ii)
Putting the value of x in equation (i), we get
(y + 6)² + y² = 468
⇒ y² + 12y + 36 + y² = 468
⇒ (2y)² +12y – 432 = 0
⇒ y² + 6y – 216 = 0
⇒ y² + 18y – 12y – 216 = 0
⇒ y(y + 18) – 12(y + 18) = 0
⇒ (y + 18)(y – 12) = 0
⇒ (y + 18) = 0 or (y – 12) = 0
Either y = -18 or y = 12
But, y ≠ -18 , as x is the side of square, which can’t be negative.
So, y = 12
Hence, the side of smaller square = 12 m Putting the value of y in equation (ii), we get Side of larger square = x = y + 6 = 12 + 6 = 18 m
How to Revise 10th Maths Chapter 4 Quadratic Equations for Exams
Schools and institutions across the world promptly acted according to a pandemic, by moving online. Tech advancement helped institutions transition physical classrooms to virtual ones in record time. For as long as I can remember, I have liked everything about mathematics – especially teaching young schoolers, I have seen some of the brilliant minds grapple to comprehend the concepts. I have seen hard-working bright-eyed students losing to perform better than average in the classroom. In this article, you will read some of the effective practices that helped many students score 100% in math of 10th standard chapter Quadratic equations.
- Step 1: NCERT Solutions for Class 10 Maths Chapter 4 helps to practice real life based Problems in Exercise 4.3.
- Step 2: Class 10 Maths Chapter 4 solutions provides the fundamental facts of Quadratic Equations.
- Step 3: NCERT Solutions Class 10 Maths Chapter 4 by applying the perfect formula for answers.
- Step 4: Class 10 Maths chapter 4 needs regular practice session after short intervals.
- Step 5: Practice Class 10 Maths chapter 4 from NCERT Textbook for exams.
Step 1: NCERT Solutions for Class 10 Maths Chapter 4 helps to practice real life based Problems in Exercise 4.3.
Step 2: Class 10 Maths Chapter 4 solutions provides the fundamental facts of Quadratic Equations.
Step 3: NCERT Solutions Class 10 Maths Chapter 4 by applying the perfect formula for answers.
Step 4: Class 10 Maths chapter 4 needs regular practice session after short intervals.
Step 5: Practice Class 10 Maths chapter 4 from NCERT Textbook for exams.
Effective Study Plan for Quadratic Equations: Day-wise Approach
Preparing for Quadratic Equations in Class 10 requires a structured approach to grasp concepts thoroughly and practice systematically. Start with understanding the basics, such as the definition of a quadratic equation, its standard form, and its graphical representation. Dedicate the first day to studying these concepts from NCERT and solving simple examples. Next, move to solving quadratic equations by factorization. Practice problems from Exercise 4.2 to understand step-by-step methods and focus on avoiding calculation errors. This method builds a strong foundation, ensuring you are ready to tackle more advanced techniques in the upcoming days.
Mastering Advanced Techniques for Quadratic Equations
On subsequent days, focus on advanced techniques like the completing the square method and the quadratic formula. These methods are crucial for solving complex problems and analyzing the nature of roots. Practice Examples 6-10 and solve questions from Exercises 4.3 and 4.4, emphasizing accuracy and speed. Allocate the last day for reviewing all methods, solving past board exam questions and identifying weak areas. Consistent revision of formulas and key concepts ensures confidence during exams. This structured day-wise plan, combined with regular practice, guarantees a solid preparation for board exams.
Why are NCERT Solutions for Class 10 Maths Chapter 4 important?
NCERT Textbook Solutions for Class 10 Mathematics Chapter 4 Quadratic Equations are crucial because they provide detailed step-by-step explanations for solving complex quadratic problems. 10th Maths chapter 4 is foundational for understanding higher-level mathematics and its applications in real life. The solutions simplify methods like factorization, completing the square (not in syllabus) and the quadratic formula, ensuring students grasp the concepts clearly. With these solutions, students can practice effectively, strengthen their problem-solving skills and gain confidence in tackling board exam questions. They cater to different learning preferences, with options like NCERT Class 10 Math Chapter 4 PDFs for convenient access.
How can I get good marks in Class 10 Maths Chapter 4 Quadratic Equations?
Student should know the methods of factorization to a quadratic equation. It will help a lot during the solution of questions in 10th Maths chapter 4. Quadratic formula is the ultimate trick to find the roots of difficult or easy format of any quadratic equation. So if someone has practiced well the factorization method and quadratic formula method, he will score better then ever in chapter 4 of class 10 mathematics.
What methods are covered in Quadratic Equations Class 10 NCERT Solutions?
The Quadratic Equations Class 10 NCERT Maths Solutions cover three main methods for solving quadratic equations: factorization, completing the square and the quadratic formula. Each method is explained thoroughly with examples, ensuring students understand when and how to apply them. 10th Math chapter 4 solutions also include exercises that analyze the nature of roots, helping students gain deeper insights. Whether solving textbook exercises or preparing for board exams, these methods provide a systematic approach. The NCERT Solutions Chapter 4 Class 10 Mathematics emphasize both theoretical understanding and practical application, making them a complete guide for mastering this topic.
How a quadratic polynomial is different from a quadratic equation in 10th Maths Chapter 4?
A polynomial of degree two is called a quadratic polynomial. When a quadratic polynomial is equated to zero, it is called a quadratic equation. A quadratic equation of the form ax² + bx + c = 0, a > 0, where a, b, c are constants and x is a variable is called a quadratic equation in the standard format.
How can the NCERT Class 10 Maths Chapter 4 PDF benefit students?
The NCERT Class 10 Mathematics Chapter 4 PDF offers students a convenient way to access solutions anytime. This digital format allows tech-savvy learners to study on their devices without needing physical textbooks. The PDF includes detailed step-by-step explanations for solving quadratic equations, worked-out math examples and additional practice questions. It’s perfect for quick revisions and self-study, especially before exams. Students can use it to focus on specific exercises, review important concepts or practice questions repeatedly. The portability and ease of use make the NCERT Simplified Solutions for Class 10 Maths Quadratic Equations PDF an invaluable resource.
In Class 10 Maths Chapter 4, which exercise is considered as the most difficult to solve?
Class 10 Maths, exercise 4.1, and 4.2 are easy to solve and having less number of questions. Exercise 4.3 is tricky to find the solutions and answers also. In this exercise most of the questions are based on application of quadratic equations.
How do Quadratic Equations NCERT Solutions Class 10 help in board exam preparation?
The Quadratic Equations NCERT Exercise Solutions Class 10 Maths play a vital role in preparing for board exams by simplifying complex mathematical concepts. Class 10th Math solutions provide clear, structured explanations and a systematic approach to solving quadratic equations. They include worked-out examples, detailed steps and practice exercises that mirror the types of questions asked in exams. The solutions help students improve their accuracy, speed and confidence. By practicing regularly with these resources, students can better understand the marking scheme and avoid common mistakes. The Class 10 Mathematics Quadratic Equations Solutions ensure thorough preparation and boost performance in exams.
What is meant by zeros of a quadratic equation in Chapter 4 of 10th Maths?
A zero of a polynomial is that real number, which when substituted for the variable makes the value of the polynomial zero. In case of a quadratic equation, the value of the variable for which LHS and RHS of the equation become equal is called a root or solution of the quadratic equation. There are three algebraic methods for finding the solution of a quadratic equation. These are (i) Factor Method (ii) Completing the square method and (iii) Using the Quadratic Formula.
What are the main topics to study in Class 10 Maths chapter 4?
In chapter 4 (Quadratic equations) of class 10th mathematics, Students will study
- 1) Meaning of Quadratic equations
- 2) Solution of a quadratic equation by factorization.
- 3) Solution of a quadratic equation by completing the square.
- 4) Solution of a quadratic equation using quadratic formula.
- 5) Nature of roots.
How many exercises are there in chapter 4 of Class 10th Maths?
There are in all 4 exercises in class 10 mathematics chapter 4 (Quadratic equations).
In first exercise (Ex 4.1), there are only 2 questions (Q1 having 8 parts and Q2 having 4 parts).
In second exercise (Ex 4.2), there are in all 6 questions.
In fourth exercise (Ex 4.3), there are in all 5 questions.
So, there are total 13 questions in class 10 mathematics chapter 4 (Quadratic equations).
In this chapter there are in all 18 examples. Examples 1, 2 are based on Ex 4.1, Examples 3, 4, 5, 6 are based on Ex 4.2, Examples 16, 17, 18 are based on Ex 4.3.
Does chapter 4 of class 10th mathematics contain optional exercise?
No, chapter 4 (Quadratic equations) of class 10th mathematics doesn’t contain any optional exercise. All the four exercises are compulsory for the exams.
How much time required to complete chapter 4 of 10th Maths?
Students need maximum 3-4 days to complete chapter 4 (Quadratic equations) of class 10th mathematics. But even after this time, revision is compulsory to retain the way to solving questions.
