Open App

Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > RD Sharma Solutions: Quadratic Equations (Exercise 4A)

Quadratic Equations (Exercise 4A) RD Sharma Solutions | Mathematics (Maths) Class 10 PDF Download

Download, print and study this document offline

Please wait while the PDF view is loading

 Page 1


 
 
1. Which of the following are quadratic equation in x?
(i) 
2
3 0 x x
(ii) 
2
5
2 3 0
2
x x
(iii) 
2
2 7 5 2 x x
(iv)  
2
1 1
2 0
3 5
x x
(v)  
2
3 4 0 x x x
(vi) 
6
3 x
x
(vii) 
2 2
2
x x
x
(viii) 
2
2
1
5 x
x
(ix) 
3
3
2 8 x x
(x) 2 3 3 2 6 1 2 x x x x
(xi) 
2
1 1
2 3 x x
x x
Sol:
(i)
2
3 x x is a quadratic polynomial
2
3 0 x x is a quadratic equation. 
(ii) Clearly, 
2
5
2 3
2
x x is a quadratic polynomial.
2
5
2 3 0
2
x x is a quadratic equation.
(iii) Clearly, 
2
2 7 5 2 x x is a quadratic polynomial.
2
2 7 5 2 0 x x is a quadratic equation. 
(iv) Clearly, 
2
1 1
2
3 5
x x is a quadratic polynomial.
2
1 1
2 0
3 5
x x is a quadratic equation. 
(v)
2
3 4 x x x contains a term with , x i.e.,
1
2
, x where 
1
2
is not a ineger.
Page 2


 
 
1. Which of the following are quadratic equation in x?
(i) 
2
3 0 x x
(ii) 
2
5
2 3 0
2
x x
(iii) 
2
2 7 5 2 x x
(iv)  
2
1 1
2 0
3 5
x x
(v)  
2
3 4 0 x x x
(vi) 
6
3 x
x
(vii) 
2 2
2
x x
x
(viii) 
2
2
1
5 x
x
(ix) 
3
3
2 8 x x
(x) 2 3 3 2 6 1 2 x x x x
(xi) 
2
1 1
2 3 x x
x x
Sol:
(i)
2
3 x x is a quadratic polynomial
2
3 0 x x is a quadratic equation. 
(ii) Clearly, 
2
5
2 3
2
x x is a quadratic polynomial.
2
5
2 3 0
2
x x is a quadratic equation.
(iii) Clearly, 
2
2 7 5 2 x x is a quadratic polynomial.
2
2 7 5 2 0 x x is a quadratic equation. 
(iv) Clearly, 
2
1 1
2
3 5
x x is a quadratic polynomial.
2
1 1
2 0
3 5
x x is a quadratic equation. 
(v)
2
3 4 x x x contains a term with , x i.e.,
1
2
, x where 
1
2
is not a ineger.
 
 
Therefore, it is not a quadratic polynomial.
2
3 4 0 x x x is not a quadratic equation.
(vi)
6
3 x
x
2
2
6 3
3 6 0
x x
x x
3
3 6 x x is not quadratic polynomial; therefore, the given equation is quadratic.  
(vii)
2 2
2
x x
x
2 3
3 2
2
2 0
x x
x x
3 2
2 x x is not a quadratic polynomial.
3 2
2 0 x x is not a quadratic equation.
(viii)
2
2
1
5 x
x
4 2
1 5 x x
4 2
5 1 0 x x
4 2
5 1 x x
is a polynomial with degree 4.
4 2
5 1 0 x x
is not a quadratic equation.
(ix)
3
3
2 8 x x
3 2 3
2
6 12 8 8
6 12 16 0
x x x x
x x
This is of the form 
2
0 a x b x c
Hence, the given equation is a quadratic equation.
(x)
2 3 3 2 6 1 2 x x x x
2 2
2 2
6 4 9 6 6 3 2
6 13 6 6 18 12
31 6 0
x x x x x
x x x x
x
This is of the form 
2
0 a x b x c
Hence, the given equation is not a quadratic equation.
(xi)
2
1 1
2 3 x x
x x
Page 3


 
 
1. Which of the following are quadratic equation in x?
(i) 
2
3 0 x x
(ii) 
2
5
2 3 0
2
x x
(iii) 
2
2 7 5 2 x x
(iv)  
2
1 1
2 0
3 5
x x
(v)  
2
3 4 0 x x x
(vi) 
6
3 x
x
(vii) 
2 2
2
x x
x
(viii) 
2
2
1
5 x
x
(ix) 
3
3
2 8 x x
(x) 2 3 3 2 6 1 2 x x x x
(xi) 
2
1 1
2 3 x x
x x
Sol:
(i)
2
3 x x is a quadratic polynomial
2
3 0 x x is a quadratic equation. 
(ii) Clearly, 
2
5
2 3
2
x x is a quadratic polynomial.
2
5
2 3 0
2
x x is a quadratic equation.
(iii) Clearly, 
2
2 7 5 2 x x is a quadratic polynomial.
2
2 7 5 2 0 x x is a quadratic equation. 
(iv) Clearly, 
2
1 1
2
3 5
x x is a quadratic polynomial.
2
1 1
2 0
3 5
x x is a quadratic equation. 
(v)
2
3 4 x x x contains a term with , x i.e.,
1
2
, x where 
1
2
is not a ineger.
 
 
Therefore, it is not a quadratic polynomial.
2
3 4 0 x x x is not a quadratic equation.
(vi)
6
3 x
x
2
2
6 3
3 6 0
x x
x x
3
3 6 x x is not quadratic polynomial; therefore, the given equation is quadratic.  
(vii)
2 2
2
x x
x
2 3
3 2
2
2 0
x x
x x
3 2
2 x x is not a quadratic polynomial.
3 2
2 0 x x is not a quadratic equation.
(viii)
2
2
1
5 x
x
4 2
1 5 x x
4 2
5 1 0 x x
4 2
5 1 x x
is a polynomial with degree 4.
4 2
5 1 0 x x
is not a quadratic equation.
(ix)
3
3
2 8 x x
3 2 3
2
6 12 8 8
6 12 16 0
x x x x
x x
This is of the form 
2
0 a x b x c
Hence, the given equation is a quadratic equation.
(x)
2 3 3 2 6 1 2 x x x x
2 2
2 2
6 4 9 6 6 3 2
6 13 6 6 18 12
31 6 0
x x x x x
x x x x
x
This is of the form 
2
0 a x b x c
Hence, the given equation is not a quadratic equation.
(xi)
2
1 1
2 3 x x
x x
 
 
2
2 2
1 1
2 3
x x
x x
2
2 2 2
4 2 3 2
4 3 2
1 2 1 3
2 1 2 2 3
2 2 1 0
x x x x
x x x x x
x x x x
This is not of the form
2
0 a x b x c
Hence, the given equation is not a quadratic equation.
2. Which of the following are the roots of 
2
3 2 1 0? x x
(i) 1 (ii)
1
3
(iii)
1
2
Sol:
The given equation is 
2
3 2 1 0 . x x
(i) 1 x
L.H.S.
2
2 1 x x
2
3 1 2 1 1
3 2 1
0
. . . R H S
Thus, 1 is a root of 
2
3 2 1 0 . x x
(ii) On subtracting 
1
3
x in the given equation, we get:
L.H.S. 
2
3 2 1 x x
2
1 1
3 2 1
3 3
1 2
3 1
9 3
1 2 3
3
0
3
0
. . . R H S
Thus,
1
3
is a root of
2
3 2 1 0 x x
Page 4


 
 
1. Which of the following are quadratic equation in x?
(i) 
2
3 0 x x
(ii) 
2
5
2 3 0
2
x x
(iii) 
2
2 7 5 2 x x
(iv)  
2
1 1
2 0
3 5
x x
(v)  
2
3 4 0 x x x
(vi) 
6
3 x
x
(vii) 
2 2
2
x x
x
(viii) 
2
2
1
5 x
x
(ix) 
3
3
2 8 x x
(x) 2 3 3 2 6 1 2 x x x x
(xi) 
2
1 1
2 3 x x
x x
Sol:
(i)
2
3 x x is a quadratic polynomial
2
3 0 x x is a quadratic equation. 
(ii) Clearly, 
2
5
2 3
2
x x is a quadratic polynomial.
2
5
2 3 0
2
x x is a quadratic equation.
(iii) Clearly, 
2
2 7 5 2 x x is a quadratic polynomial.
2
2 7 5 2 0 x x is a quadratic equation. 
(iv) Clearly, 
2
1 1
2
3 5
x x is a quadratic polynomial.
2
1 1
2 0
3 5
x x is a quadratic equation. 
(v)
2
3 4 x x x contains a term with , x i.e.,
1
2
, x where 
1
2
is not a ineger.
 
 
Therefore, it is not a quadratic polynomial.
2
3 4 0 x x x is not a quadratic equation.
(vi)
6
3 x
x
2
2
6 3
3 6 0
x x
x x
3
3 6 x x is not quadratic polynomial; therefore, the given equation is quadratic.  
(vii)
2 2
2
x x
x
2 3
3 2
2
2 0
x x
x x
3 2
2 x x is not a quadratic polynomial.
3 2
2 0 x x is not a quadratic equation.
(viii)
2
2
1
5 x
x
4 2
1 5 x x
4 2
5 1 0 x x
4 2
5 1 x x
is a polynomial with degree 4.
4 2
5 1 0 x x
is not a quadratic equation.
(ix)
3
3
2 8 x x
3 2 3
2
6 12 8 8
6 12 16 0
x x x x
x x
This is of the form 
2
0 a x b x c
Hence, the given equation is a quadratic equation.
(x)
2 3 3 2 6 1 2 x x x x
2 2
2 2
6 4 9 6 6 3 2
6 13 6 6 18 12
31 6 0
x x x x x
x x x x
x
This is of the form 
2
0 a x b x c
Hence, the given equation is not a quadratic equation.
(xi)
2
1 1
2 3 x x
x x
 
 
2
2 2
1 1
2 3
x x
x x
2
2 2 2
4 2 3 2
4 3 2
1 2 1 3
2 1 2 2 3
2 2 1 0
x x x x
x x x x x
x x x x
This is not of the form
2
0 a x b x c
Hence, the given equation is not a quadratic equation.
2. Which of the following are the roots of 
2
3 2 1 0? x x
(i) 1 (ii)
1
3
(iii)
1
2
Sol:
The given equation is 
2
3 2 1 0 . x x
(i) 1 x
L.H.S.
2
2 1 x x
2
3 1 2 1 1
3 2 1
0
. . . R H S
Thus, 1 is a root of 
2
3 2 1 0 . x x
(ii) On subtracting 
1
3
x in the given equation, we get:
L.H.S. 
2
3 2 1 x x
2
1 1
3 2 1
3 3
1 2
3 1
9 3
1 2 3
3
0
3
0
. . . R H S
Thus,
1
3
is a root of
2
3 2 1 0 x x
 
 
(iii) On subtracting 
1
2
x in the given equation, we get
L.H.S.
2
3 2 1 x x
2
1 1
3 2 1
2 2
1
3 1 1
4
3
2
4
3 8
4
5
0
4
Thus, . . . . . L H S R H S
Hence, 
1
2
is a solution of 
2
3 2 1 0 . x x
3. Find the value of k for which 1 x is a root of the equation
2
3 0. x k x
Sol:
It is given that 1 x is a root of 
2
3 0 . x k x
Therefore, 1 x must satisfy the equation.
2
1 1 3 0
4 0
4
k
k
k
Hence, the required value of k is 4.
4. Find the value of a and b for which
3
4
x and 2 x are the roots of the equation
2
6 0 a x b x
Sol:
It is given that 
3
4
is a root of 
2
6 0; a x b x therefore, we have:
2
3 3
6 0
4 4
a b
Page 5


 
 
1. Which of the following are quadratic equation in x?
(i) 
2
3 0 x x
(ii) 
2
5
2 3 0
2
x x
(iii) 
2
2 7 5 2 x x
(iv)  
2
1 1
2 0
3 5
x x
(v)  
2
3 4 0 x x x
(vi) 
6
3 x
x
(vii) 
2 2
2
x x
x
(viii) 
2
2
1
5 x
x
(ix) 
3
3
2 8 x x
(x) 2 3 3 2 6 1 2 x x x x
(xi) 
2
1 1
2 3 x x
x x
Sol:
(i)
2
3 x x is a quadratic polynomial
2
3 0 x x is a quadratic equation. 
(ii) Clearly, 
2
5
2 3
2
x x is a quadratic polynomial.
2
5
2 3 0
2
x x is a quadratic equation.
(iii) Clearly, 
2
2 7 5 2 x x is a quadratic polynomial.
2
2 7 5 2 0 x x is a quadratic equation. 
(iv) Clearly, 
2
1 1
2
3 5
x x is a quadratic polynomial.
2
1 1
2 0
3 5
x x is a quadratic equation. 
(v)
2
3 4 x x x contains a term with , x i.e.,
1
2
, x where 
1
2
is not a ineger.
 
 
Therefore, it is not a quadratic polynomial.
2
3 4 0 x x x is not a quadratic equation.
(vi)
6
3 x
x
2
2
6 3
3 6 0
x x
x x
3
3 6 x x is not quadratic polynomial; therefore, the given equation is quadratic.  
(vii)
2 2
2
x x
x
2 3
3 2
2
2 0
x x
x x
3 2
2 x x is not a quadratic polynomial.
3 2
2 0 x x is not a quadratic equation.
(viii)
2
2
1
5 x
x
4 2
1 5 x x
4 2
5 1 0 x x
4 2
5 1 x x
is a polynomial with degree 4.
4 2
5 1 0 x x
is not a quadratic equation.
(ix)
3
3
2 8 x x
3 2 3
2
6 12 8 8
6 12 16 0
x x x x
x x
This is of the form 
2
0 a x b x c
Hence, the given equation is a quadratic equation.
(x)
2 3 3 2 6 1 2 x x x x
2 2
2 2
6 4 9 6 6 3 2
6 13 6 6 18 12
31 6 0
x x x x x
x x x x
x
This is of the form 
2
0 a x b x c
Hence, the given equation is not a quadratic equation.
(xi)
2
1 1
2 3 x x
x x
 
 
2
2 2
1 1
2 3
x x
x x
2
2 2 2
4 2 3 2
4 3 2
1 2 1 3
2 1 2 2 3
2 2 1 0
x x x x
x x x x x
x x x x
This is not of the form
2
0 a x b x c
Hence, the given equation is not a quadratic equation.
2. Which of the following are the roots of 
2
3 2 1 0? x x
(i) 1 (ii)
1
3
(iii)
1
2
Sol:
The given equation is 
2
3 2 1 0 . x x
(i) 1 x
L.H.S.
2
2 1 x x
2
3 1 2 1 1
3 2 1
0
. . . R H S
Thus, 1 is a root of 
2
3 2 1 0 . x x
(ii) On subtracting 
1
3
x in the given equation, we get:
L.H.S. 
2
3 2 1 x x
2
1 1
3 2 1
3 3
1 2
3 1
9 3
1 2 3
3
0
3
0
. . . R H S
Thus,
1
3
is a root of
2
3 2 1 0 x x
 
 
(iii) On subtracting 
1
2
x in the given equation, we get
L.H.S.
2
3 2 1 x x
2
1 1
3 2 1
2 2
1
3 1 1
4
3
2
4
3 8
4
5
0
4
Thus, . . . . . L H S R H S
Hence, 
1
2
is a solution of 
2
3 2 1 0 . x x
3. Find the value of k for which 1 x is a root of the equation
2
3 0. x k x
Sol:
It is given that 1 x is a root of 
2
3 0 . x k x
Therefore, 1 x must satisfy the equation.
2
1 1 3 0
4 0
4
k
k
k
Hence, the required value of k is 4.
4. Find the value of a and b for which
3
4
x and 2 x are the roots of the equation
2
6 0 a x b x
Sol:
It is given that 
3
4
is a root of 
2
6 0; a x b x therefore, we have:
2
3 3
6 0
4 4
a b
 
 
9 3
6
16 4
9 12
6
16
9 12 96 0
a b
a b
a b
3 4 32 .......... a b i
Again, 2 is a root of 
2
6 0; a x b x therefore, we have:
2
2 2 6 0
4 2 6
2 3 .........
a b
a b
a b i i
On multiplying (ii) by 4 and adding the result with (i), we get:
3 4 8 4 32 12
11 44
a b a b
a
4 a
Putting the value of a in (ii), we get:
2 4 3
8 3
5
b
b
b
Hence, the required values of a and b are 4 and 5, respectively.
5. 2 3 3 1 0 x x
Sol:
2 3 3 1 0 x x
2 3 0 3 1 0
2 3 3 1
3 1
2 3
x or x
x or x
x or x
Hence the roots of the given equation are 
3 1
.
2 3
a n d
6.
2
4 5 0 x x
Sol:
2
4 5 0 x x
4 5 0 x x
0 4 5 0 x o r x

	Mathematics (Maths) Class 10 123 videos\|457 docs\|77 tests

Mathematics (Maths) Class 10

123 videos|457 docs|77 tests

Join Course for Free

Top Courses for Class 10

View all

FAQs on Quadratic Equations (Exercise 4A) RD Sharma Solutions - Mathematics (Maths) Class 10

1. What are quadratic equations?

Ans. Quadratic equations are algebraic equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and x represents an unknown variable. These equations have a maximum of two solutions, which can be found using various methods such as factoring, completing the square, or using the quadratic formula.

2. How do you solve quadratic equations by factoring?

Ans. To solve quadratic equations by factoring, follow these steps: 1. Write the quadratic equation in the form ax^2 + bx + c = 0. 2. Factor the equation into two binomials. 3. Set each binomial equal to zero and solve for x. 4. The solutions obtained are the values of x that satisfy the quadratic equation.

3. What is the quadratic formula and how is it used to solve quadratic equations?

Ans. The quadratic formula is given by x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0. To use the quadratic formula, substitute the values of a, b, and c into the formula and simplify. The solutions obtained using the quadratic formula are the roots of the quadratic equation.

4. Can quadratic equations have more than two solutions?

Ans. No, quadratic equations can have a maximum of two solutions. This is because a quadratic equation is a second-degree polynomial, and a polynomial of degree n can have a maximum of n solutions. In the case of quadratic equations, the solutions can be real or complex, but there will always be at most two distinct solutions.

5. How can quadratic equations be used in real-life applications?

Ans. Quadratic equations have various real-life applications, including physics, engineering, finance, and computer graphics. For example, they can be used to model the trajectory of a projectile, calculate the maximum or minimum value of a quantity, analyze the profit or loss in a business, or design curved shapes in computer animations. By solving quadratic equations, we can find important information and make predictions in these practical scenarios.

Related Exams

Class 10

About this Document

	4.84/5 Rating
	Nov 19, 2024 Last updated

Document Description: RD Sharma Solutions: Quadratic Equations (Exercise 4A) for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The notes and questions for RD Sharma Solutions: Quadratic Equations (Exercise 4A) have been prepared according to the Class 10 exam syllabus. Information about RD Sharma Solutions: Quadratic Equations (Exercise 4A) covers topics like and RD Sharma Solutions: Quadratic Equations (Exercise 4A) Example, for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Solutions: Quadratic Equations (Exercise 4A).

Introduction of RD Sharma Solutions: Quadratic Equations (Exercise 4A) in English is available as part of our Mathematics (Maths) Class 10 for Class 10 & RD Sharma Solutions: Quadratic Equations (Exercise 4A) in Hindi for Mathematics (Maths) Class 10 course. Download more important topics related with notes, lectures and mock test series for Class 10 Exam by signing up for free. Class 10: Quadratic Equations (Exercise 4A) RD Sharma Solutions | Mathematics (Maths) Class 10

Description

Full syllabus notes, lecture & questions for Quadratic Equations (Exercise 4A) RD Sharma Solutions | Mathematics (Maths) Class 10 - Class 10 | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 10 | Best notes, free PDF download

Information about RD Sharma Solutions: Quadratic Equations (Exercise 4A)

In this doc you can find the meaning of RD Sharma Solutions: Quadratic Equations (Exercise 4A) defined & explained in the simplest way possible. Besides explaining types of RD Sharma Solutions: Quadratic Equations (Exercise 4A) theory, EduRev gives you an ample number of questions to practice RD Sharma Solutions: Quadratic Equations (Exercise 4A) tests, examples and also practice Class 10 tests

	Mathematics (Maths) Class 10 123 videos\|457 docs\|77 tests

Mathematics (Maths) Class 10

123 videos|457 docs|77 tests

Join Course for Free

Download as PDF

Explore Courses for Class 10 exam

Top Courses for Class 10

Explore Courses

Signup for Free!

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.

Start learning for Free

10M+ students study on EduRev

Previous Year Questions with Solutions

Viva Questions

MCQs

shortcuts and tricks

Exam

Quadratic Equations (Exercise 4A) RD Sharma Solutions | Mathematics (Maths) Class 10

Objective type Questions

pdf

mock tests for examination

Extra Questions

ppt

Summary

Sample Paper

video lectures

Semester Notes

Important questions

past year papers

Free

Quadratic Equations (Exercise 4A) RD Sharma Solutions | Mathematics (Maths) Class 10

practice quizzes

study material

;

Additional Information about RD Sharma Solutions: Quadratic Equations (Exercise 4A) for Class 10 Preparation

RD Sharma Solutions: Quadratic Equations (Exercise 4A) Free PDF Download

The RD Sharma Solutions: Quadratic Equations (Exercise 4A) is an invaluable resource that delves deep into the core of the Class 10 exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the RD Sharma Solutions: Quadratic Equations (Exercise 4A) now and kickstart your journey towards success in the Class 10 exam.

Importance of RD Sharma Solutions: Quadratic Equations (Exercise 4A)

The importance of RD Sharma Solutions: Quadratic Equations (Exercise 4A) cannot be overstated, especially for Class 10 aspirants. This document holds the key to success in the Class 10 exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

RD Sharma Solutions: Quadratic Equations (Exercise 4A) Notes

RD Sharma Solutions: Quadratic Equations (Exercise 4A) Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to RD Sharma Solutions: Quadratic Equations (Exercise 4A). It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, RD Sharma Solutions: Quadratic Equations (Exercise 4A) Notes on EduRev are your ultimate resource for success.

RD Sharma Solutions: Quadratic Equations (Exercise 4A) Class 10 Questions

The "RD Sharma Solutions: Quadratic Equations (Exercise 4A) Class 10 Questions" guide is a valuable resource for all aspiring students preparing for the Class 10 exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study RD Sharma Solutions: Quadratic Equations (Exercise 4A) on the App

Students of Class 10 can study RD Sharma Solutions: Quadratic Equations (Exercise 4A) alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the RD Sharma Solutions: Quadratic Equations (Exercise 4A), students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of RD Sharma Solutions: Quadratic Equations (Exercise 4A) is prepared as per the latest Class 10 syllabus.

Education Revolution