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 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=?

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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).

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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.

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

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