Open App

Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > RS Aggarwal Solutions: Quadratic Equations (Exercise 4F)

RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) | 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 is a quadratic equation?
(a)
3
3 2 0 x x (b) 
2
1
x x
x
(c)  
2
2
1
5 x
x
(d)
2
2
2 5 1 x x x
Answer: (d) 
2
2
2 5 1 x x x
Sol:
A quadratic equation is the equation with degree 2.
2
2
2 2
2 2
2 5 1
2 5 2 1
2 5 2 1 0
x x x
x x x x
x x x x
2
3 1 0, x x which is a quadratic equation
2. Which of the following is a quadratic equation?
(a)
2
2
1 2 3 x x (b)
3
3 2
1 x x x
(c) 
2
2 3 5 2 3 x x x (d) None of these
Answer: (b) 
3
3 2
1 x x x
Sol:
3
3 2
3 2 3 2
1
3 3 1
x x x
x x x x x
2
2 3 1 0, x x which is a quadratic equation
3. Which of the following is not a quadratic equation?
(a) 
2 2
3 5 x x x (b) 
2
2
2 2 5 x x
(c)
2
2
2 3 2 6 x x (d)
2
2
1 3 2 x x x
Answer: (c) 
2
2
2 3 2 6 x x
Sol:
2
2
2
2 3 2 6
2 9 6 2 2 6
x x
x x x
6 2 3 0, x which is not a quadratic equation
Page 2


 
1. Which of the following is a quadratic equation?
(a)
3
3 2 0 x x (b) 
2
1
x x
x
(c)  
2
2
1
5 x
x
(d)
2
2
2 5 1 x x x
Answer: (d) 
2
2
2 5 1 x x x
Sol:
A quadratic equation is the equation with degree 2.
2
2
2 2
2 2
2 5 1
2 5 2 1
2 5 2 1 0
x x x
x x x x
x x x x
2
3 1 0, x x which is a quadratic equation
2. Which of the following is a quadratic equation?
(a)
2
2
1 2 3 x x (b)
3
3 2
1 x x x
(c) 
2
2 3 5 2 3 x x x (d) None of these
Answer: (b) 
3
3 2
1 x x x
Sol:
3
3 2
3 2 3 2
1
3 3 1
x x x
x x x x x
2
2 3 1 0, x x which is a quadratic equation
3. Which of the following is not a quadratic equation?
(a) 
2 2
3 5 x x x (b) 
2
2
2 2 5 x x
(c)
2
2
2 3 2 6 x x (d)
2
2
1 3 2 x x x
Answer: (c) 
2
2
2 3 2 6 x x
Sol:
2
2
2
2 3 2 6
2 9 6 2 2 6
x x
x x x
6 2 3 0, x which is not a quadratic equation
 
4. If 3 x is a solution of the equation
2
3 1 9 0, x k x then ? k
(a) 11 (b) 11 (c) 13 (d) 13
Answer: (b) 11
Sol:
It is given that 3 x is a solution of 
2
3 1 9 0; x k x therefore, we have:
2
3 3 1 3 9 0
27 3 1 9 0
3 1 36
1 12
11
k
k
k
k
k
5. If one root of the equation 
2
2 6 0 x a x is 2 then a=?
(a) 7 (b) -7 (c) 
7
2
(d) 
7
2
Answer: (b) -7
Sol:
It is given that one root of the equation 
2
2 6 0 x a x is 2.
2
2 2 2 6 0
2 14 0
7
a
a
a
6. The sum of the roots of the equation
2
6 2 0 x x is 
(a) 2 (b) -2 (c) 6 (d) -6
Answer: (b) -2
Sol:
Sum of the roots of the equation 
2
6 2 0 x x is
6
6,
1
b
a
where and are the roots of the equation.
7. If the product of the roots of the equation
2
3 10 x x k is -2 then the value of k is 
(a) -2 (b) -8 (c) 8 (d) 12
Answer: (c) 8 
Sol:
It is given that the product of the roots of the equation 
2
3 10 x x k is . 2
The equation can be rewritten as:
2
3 10 0 x x k
Page 3


 
1. Which of the following is a quadratic equation?
(a)
3
3 2 0 x x (b) 
2
1
x x
x
(c)  
2
2
1
5 x
x
(d)
2
2
2 5 1 x x x
Answer: (d) 
2
2
2 5 1 x x x
Sol:
A quadratic equation is the equation with degree 2.
2
2
2 2
2 2
2 5 1
2 5 2 1
2 5 2 1 0
x x x
x x x x
x x x x
2
3 1 0, x x which is a quadratic equation
2. Which of the following is a quadratic equation?
(a)
2
2
1 2 3 x x (b)
3
3 2
1 x x x
(c) 
2
2 3 5 2 3 x x x (d) None of these
Answer: (b) 
3
3 2
1 x x x
Sol:
3
3 2
3 2 3 2
1
3 3 1
x x x
x x x x x
2
2 3 1 0, x x which is a quadratic equation
3. Which of the following is not a quadratic equation?
(a) 
2 2
3 5 x x x (b) 
2
2
2 2 5 x x
(c)
2
2
2 3 2 6 x x (d)
2
2
1 3 2 x x x
Answer: (c) 
2
2
2 3 2 6 x x
Sol:
2
2
2
2 3 2 6
2 9 6 2 2 6
x x
x x x
6 2 3 0, x which is not a quadratic equation
 
4. If 3 x is a solution of the equation
2
3 1 9 0, x k x then ? k
(a) 11 (b) 11 (c) 13 (d) 13
Answer: (b) 11
Sol:
It is given that 3 x is a solution of 
2
3 1 9 0; x k x therefore, we have:
2
3 3 1 3 9 0
27 3 1 9 0
3 1 36
1 12
11
k
k
k
k
k
5. If one root of the equation 
2
2 6 0 x a x is 2 then a=?
(a) 7 (b) -7 (c) 
7
2
(d) 
7
2
Answer: (b) -7
Sol:
It is given that one root of the equation 
2
2 6 0 x a x is 2.
2
2 2 2 6 0
2 14 0
7
a
a
a
6. The sum of the roots of the equation
2
6 2 0 x x is 
(a) 2 (b) -2 (c) 6 (d) -6
Answer: (b) -2
Sol:
Sum of the roots of the equation 
2
6 2 0 x x is
6
6,
1
b
a
where and are the roots of the equation.
7. If the product of the roots of the equation
2
3 10 x x k is -2 then the value of k is 
(a) -2 (b) -8 (c) 8 (d) 12
Answer: (c) 8 
Sol:
It is given that the product of the roots of the equation 
2
3 10 x x k is . 2
The equation can be rewritten as:
2
3 10 0 x x k
 
 
Product of the roots of a quadratic equation
c
a
2
c
a
10
2
1
8
k
k
8. The ratio of the sum and product of the roots of the equation 
2
7 12 18 0 x x is
(a) 7 :12 (b) 7 :18 (c) 3 : 2 (d) 2 : 3
Answer : (d) 2 : 3
Sol:
Given:
2
7 12 18 0 x x
12 18
,
7 7
and where and are the roots of the equation
Ratio of the sum and product of the roots
12 18
:
7 7
12:18
2:3
9. If one root of the equation 
2
3 10 3 0 x x is 
1
3
then the other root is 
(a) 
1
3
(b) 
1
3
(c) -3 (d)3
Answer: (d)3
Sol:
Given:
2
3 10 3 0 x x
One root of the equation is 
1
.
3
Let the other root be .
Product of the roots
c
a
1 3
3 3
3
10. If one root of 
2
5 13 0 x x k be the reciprocal of the other root then the value of k is
Page 4


 
1. Which of the following is a quadratic equation?
(a)
3
3 2 0 x x (b) 
2
1
x x
x
(c)  
2
2
1
5 x
x
(d)
2
2
2 5 1 x x x
Answer: (d) 
2
2
2 5 1 x x x
Sol:
A quadratic equation is the equation with degree 2.
2
2
2 2
2 2
2 5 1
2 5 2 1
2 5 2 1 0
x x x
x x x x
x x x x
2
3 1 0, x x which is a quadratic equation
2. Which of the following is a quadratic equation?
(a)
2
2
1 2 3 x x (b)
3
3 2
1 x x x
(c) 
2
2 3 5 2 3 x x x (d) None of these
Answer: (b) 
3
3 2
1 x x x
Sol:
3
3 2
3 2 3 2
1
3 3 1
x x x
x x x x x
2
2 3 1 0, x x which is a quadratic equation
3. Which of the following is not a quadratic equation?
(a) 
2 2
3 5 x x x (b) 
2
2
2 2 5 x x
(c)
2
2
2 3 2 6 x x (d)
2
2
1 3 2 x x x
Answer: (c) 
2
2
2 3 2 6 x x
Sol:
2
2
2
2 3 2 6
2 9 6 2 2 6
x x
x x x
6 2 3 0, x which is not a quadratic equation
 
4. If 3 x is a solution of the equation
2
3 1 9 0, x k x then ? k
(a) 11 (b) 11 (c) 13 (d) 13
Answer: (b) 11
Sol:
It is given that 3 x is a solution of 
2
3 1 9 0; x k x therefore, we have:
2
3 3 1 3 9 0
27 3 1 9 0
3 1 36
1 12
11
k
k
k
k
k
5. If one root of the equation 
2
2 6 0 x a x is 2 then a=?
(a) 7 (b) -7 (c) 
7
2
(d) 
7
2
Answer: (b) -7
Sol:
It is given that one root of the equation 
2
2 6 0 x a x is 2.
2
2 2 2 6 0
2 14 0
7
a
a
a
6. The sum of the roots of the equation
2
6 2 0 x x is 
(a) 2 (b) -2 (c) 6 (d) -6
Answer: (b) -2
Sol:
Sum of the roots of the equation 
2
6 2 0 x x is
6
6,
1
b
a
where and are the roots of the equation.
7. If the product of the roots of the equation
2
3 10 x x k is -2 then the value of k is 
(a) -2 (b) -8 (c) 8 (d) 12
Answer: (c) 8 
Sol:
It is given that the product of the roots of the equation 
2
3 10 x x k is . 2
The equation can be rewritten as:
2
3 10 0 x x k
 
 
Product of the roots of a quadratic equation
c
a
2
c
a
10
2
1
8
k
k
8. The ratio of the sum and product of the roots of the equation 
2
7 12 18 0 x x is
(a) 7 :12 (b) 7 :18 (c) 3 : 2 (d) 2 : 3
Answer : (d) 2 : 3
Sol:
Given:
2
7 12 18 0 x x
12 18
,
7 7
and where and are the roots of the equation
Ratio of the sum and product of the roots
12 18
:
7 7
12:18
2:3
9. If one root of the equation 
2
3 10 3 0 x x is 
1
3
then the other root is 
(a) 
1
3
(b) 
1
3
(c) -3 (d)3
Answer: (d)3
Sol:
Given:
2
3 10 3 0 x x
One root of the equation is 
1
.
3
Let the other root be .
Product of the roots
c
a
1 3
3 3
3
10. If one root of 
2
5 13 0 x x k be the reciprocal of the other root then the value of k is
 
(a) 0 (b) 1 (c)2(d)5
Answer: (d)5
Sol:
Let the roots of the equation 
2
3
be and 
1
.
Product of the roots 
c
a
1
5
5
5
k
k
a
k
11. If the sum of the roots of the equation 
2
2 3 0 k x x k is equal to their product then the value
of k
(a) 
1
3
(b) 
1
3
(c)
2
3
(d)
2
3
Answer: (d) 
2
3
Sol:
Given:
2
2 3 0 k x x k
Sum of the roots = Product of the roots
2 3
3 2
2
3
k
k k
k
k
12. The roots of a quadratic equation are 5 and -2. Then, the equation is
(a) 
2
3 10 0 x x (b) 
2
3 10 0 x x (c) 
2
3 10 0 x x (d)
2
3 10 0 x x
Answer: (b) 
2
3 10 0 x x
Sol:
It is given that the roots of the quadratic equation are 5 and . 2
Then, the equation is:
2
2
5 2 5 2 0
3 10 0
x x
x x
13. If the sum of the roots of a quadratic equation is 6 and their product is 6, the equation is
Page 5


 
1. Which of the following is a quadratic equation?
(a)
3
3 2 0 x x (b) 
2
1
x x
x
(c)  
2
2
1
5 x
x
(d)
2
2
2 5 1 x x x
Answer: (d) 
2
2
2 5 1 x x x
Sol:
A quadratic equation is the equation with degree 2.
2
2
2 2
2 2
2 5 1
2 5 2 1
2 5 2 1 0
x x x
x x x x
x x x x
2
3 1 0, x x which is a quadratic equation
2. Which of the following is a quadratic equation?
(a)
2
2
1 2 3 x x (b)
3
3 2
1 x x x
(c) 
2
2 3 5 2 3 x x x (d) None of these
Answer: (b) 
3
3 2
1 x x x
Sol:
3
3 2
3 2 3 2
1
3 3 1
x x x
x x x x x
2
2 3 1 0, x x which is a quadratic equation
3. Which of the following is not a quadratic equation?
(a) 
2 2
3 5 x x x (b) 
2
2
2 2 5 x x
(c)
2
2
2 3 2 6 x x (d)
2
2
1 3 2 x x x
Answer: (c) 
2
2
2 3 2 6 x x
Sol:
2
2
2
2 3 2 6
2 9 6 2 2 6
x x
x x x
6 2 3 0, x which is not a quadratic equation
 
4. If 3 x is a solution of the equation
2
3 1 9 0, x k x then ? k
(a) 11 (b) 11 (c) 13 (d) 13
Answer: (b) 11
Sol:
It is given that 3 x is a solution of 
2
3 1 9 0; x k x therefore, we have:
2
3 3 1 3 9 0
27 3 1 9 0
3 1 36
1 12
11
k
k
k
k
k
5. If one root of the equation 
2
2 6 0 x a x is 2 then a=?
(a) 7 (b) -7 (c) 
7
2
(d) 
7
2
Answer: (b) -7
Sol:
It is given that one root of the equation 
2
2 6 0 x a x is 2.
2
2 2 2 6 0
2 14 0
7
a
a
a
6. The sum of the roots of the equation
2
6 2 0 x x is 
(a) 2 (b) -2 (c) 6 (d) -6
Answer: (b) -2
Sol:
Sum of the roots of the equation 
2
6 2 0 x x is
6
6,
1
b
a
where and are the roots of the equation.
7. If the product of the roots of the equation
2
3 10 x x k is -2 then the value of k is 
(a) -2 (b) -8 (c) 8 (d) 12
Answer: (c) 8 
Sol:
It is given that the product of the roots of the equation 
2
3 10 x x k is . 2
The equation can be rewritten as:
2
3 10 0 x x k
 
 
Product of the roots of a quadratic equation
c
a
2
c
a
10
2
1
8
k
k
8. The ratio of the sum and product of the roots of the equation 
2
7 12 18 0 x x is
(a) 7 :12 (b) 7 :18 (c) 3 : 2 (d) 2 : 3
Answer : (d) 2 : 3
Sol:
Given:
2
7 12 18 0 x x
12 18
,
7 7
and where and are the roots of the equation
Ratio of the sum and product of the roots
12 18
:
7 7
12:18
2:3
9. If one root of the equation 
2
3 10 3 0 x x is 
1
3
then the other root is 
(a) 
1
3
(b) 
1
3
(c) -3 (d)3
Answer: (d)3
Sol:
Given:
2
3 10 3 0 x x
One root of the equation is 
1
.
3
Let the other root be .
Product of the roots
c
a
1 3
3 3
3
10. If one root of 
2
5 13 0 x x k be the reciprocal of the other root then the value of k is
 
(a) 0 (b) 1 (c)2(d)5
Answer: (d)5
Sol:
Let the roots of the equation 
2
3
be and 
1
.
Product of the roots 
c
a
1
5
5
5
k
k
a
k
11. If the sum of the roots of the equation 
2
2 3 0 k x x k is equal to their product then the value
of k
(a) 
1
3
(b) 
1
3
(c)
2
3
(d)
2
3
Answer: (d) 
2
3
Sol:
Given:
2
2 3 0 k x x k
Sum of the roots = Product of the roots
2 3
3 2
2
3
k
k k
k
k
12. The roots of a quadratic equation are 5 and -2. Then, the equation is
(a) 
2
3 10 0 x x (b) 
2
3 10 0 x x (c) 
2
3 10 0 x x (d)
2
3 10 0 x x
Answer: (b) 
2
3 10 0 x x
Sol:
It is given that the roots of the quadratic equation are 5 and . 2
Then, the equation is:
2
2
5 2 5 2 0
3 10 0
x x
x x
13. If the sum of the roots of a quadratic equation is 6 and their product is 6, the equation is
 
(a)
2
6 6 0 x x (b)
2
6 6 0 x x (c)
2
6 6 0 x x (d) 
2
6 6 0 x x
Answer: (a) 
2
6 6 0 x x
Sol:
Given:
Sum of roots = 6
Product of roots = 6
Thus, the equation is:
2
6 6 0 x x
14. If a n d are the roots of the equation 
2
3 8 2 0 x x then 
1 1
?
(a) 
3
8
(b)
2
3
(c) -4 (d) 4 
Answer: (c) -4
Sol:
It is given that and are the roots of the equation 
2
3 8 2 0 x x
8 2
3 3
and
8
1 1
3
4
2
3
15. The roots of the equation 
2
0 a x b x c will be reciprocal each other if
(a) a = b (b) b = c (c) c = a (d) none of these
Answer: (c) c = a
Sol:
Let the roots of the equation 
2
0 a x b x c be and 
1
.
Product of the roots 
1
1
1
c
a
c a
16. If the roots of the equation 
2
0 a x b x c are equal then c=?

	Mathematics (Maths) Class 10 126 videos\|457 docs\|75 tests

Mathematics (Maths) Class 10

126 videos|457 docs|75 tests

Join Course for Free

Top Courses for Class 10

View all

Related Exams

Class 10

About this Document

	4.74/5 Rating
	Dec 23, 2024 Last updated

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

Introduction of RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) in English is available as part of our Mathematics (Maths) Class 10 for Class 10 & RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) 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: RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) | Mathematics (Maths) Class 10

Description

Full syllabus notes, lecture & questions for RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) | 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 RS Aggarwal Solutions: Quadratic Equations (Exercise 4F)

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

	Mathematics (Maths) Class 10 126 videos\|457 docs\|75 tests

Mathematics (Maths) Class 10

126 videos|457 docs|75 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

Extra Questions

pdf

Viva Questions

video lectures

practice quizzes

Semester Notes

past year papers

MCQs

Sample Paper

Exam

Important questions

RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) | Mathematics (Maths) Class 10

mock tests for examination

RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) | Mathematics (Maths) Class 10

ppt

shortcuts and tricks

Previous Year Questions with Solutions

Free

Objective type Questions

study material

Summary

;

Additional Information about RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) for Class 10 Preparation

RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) Free PDF Download

The RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) 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 RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) now and kickstart your journey towards success in the Class 10 exam.

Importance of RS Aggarwal Solutions: Quadratic Equations (Exercise 4F)

The importance of RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) 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.

RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) Notes

RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to RS Aggarwal Solutions: Quadratic Equations (Exercise 4F). 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, RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) Notes on EduRev are your ultimate resource for success.

RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) Class 10 Questions

The "RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) 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 RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) on the App

Students of Class 10 can study RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the RS Aggarwal Solutions: Quadratic Equations (Exercise 4F), 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 RS Aggarwal Solutions: Quadratic Equations (Exercise 4F) is prepared as per the latest Class 10 syllabus.

Education Revolution