CBSE Class 10 Mathematics Quadratic Equation Worksheet Set D

Read and download the CBSE Class 10 Mathematics Quadratic Equation Worksheet Set D in PDF format. We have provided exhaustive and printable Class 10 Mathematics worksheets for Chapter 4 Quadratic Equation, designed by expert teachers. These resources align with the 2025-26 syllabus and examination patterns issued by NCERT, CBSE, and KVS, helping students master all important chapter topics.

Chapter-wise Worksheet for Class 10 Mathematics Chapter 4 Quadratic Equation

Students of Class 10 should use this Mathematics practice paper to check their understanding of Chapter 4 Quadratic Equation as it includes essential problems and detailed solutions. Regular self-testing with these will help you achieve higher marks in your school tests and final examinations.

Class 10 Mathematics Chapter 4 Quadratic Equation Worksheet with Answers

 

QUADRATIC EQUATIONS

Q.- Without solving, examine the nature of roots of the equations :
(i) 2x2 + 2x + 3 = 0
(ii) 2x2 – 7x + 3 = 0
(iii) x2 – 5x – 2 = 0
(iv) 4x2 – 4x + 1 = 0
 
Sol. (i) Comparing 2x2 + 2x + 3 = 0
with ax2 + bx + c = 0; we get : a = 2, b = 2 and c = 3
D = b2 – 4ac = (2)2 – 4 × 2 × 3 = 4 – 24
= – 20; which is negative.
∴The roots of the given equation are imaginary.
 
(ii) Comparing 2x2 – 7x + 3 = 0
with ax2 + bx + c = 0;
we get : a = 2, b = – 7 and c = 3
D = b2 – 4ac = (–7)2 – 4 × 2 × 3
= 49 – 24 = 25, which is perfect square.
∴The roots of the given equation are rational and unequal.
 
(iii) Comparing x2 – 5x – 2 = 0
with ax2 + bx + c = 0;
we get : a = 1, b = – 5 and c = – 2
D = b2 – 4ac = (–5)2 – 4 × 1 × – 2
= 25 + 8 = 33 ; which is positive but not a perfect square.
∴The roots of the given equation are irrational and unequal.
 
(iv) Comparing 4x2 – 4x + 1 = 0
with ax2 + bx + c = 0;
we get : a = 4, b = – 4, and c = 1
D = b2 – 4ac = (–4)2 – 4 × 4 × 1
= 16 – 16 = 0
∴ Roots are real and equal
 
Q.- For what value of m, are the roots of the equation (3m + 1) x2 + (11 + m) x + 9 = 0 equal?
 
Sol. Comparing the given equation
with ax2 + bx + c = 0;
we get : a = 3m + 1, b = 11 + m and c = 9
∴  Discriminant, D = b2 – 4ac
= (11 + m)2 – 4(3m + 1) × 9
= 121 + 22m + m2 – 108 m – 36
= m2 – 86m + 85
= m2 – 85m – m + 85
= m(m – 85) – 1 (m – 85)
= (m – 85) (m – 1)
Since the roots are equal, D = 0
=> (m – 85) (m – 1) = 0
=> m – 85 = 0 or m – 1 = 0
=> m = 85 or m = 1 
 
Q.- If one of the roots of the quadratic equation 2x2 + px + 4 = 0 is 2, find the the value of p. also find the value of the other roots.
 
Sol. As, 2 is one of the roots, x = 2 will satisfy the
equation 2x2 + px + 4 = 0
=> 2(2)2 + p(2) + 4 = 0
=> 8 + 2p + 4 = 0
i.e., 2p = – 12 and p = – 6
Substituting p = – 6 in the equation
2x2 + px + 4 = 0; we get : 2x2 – 6x + 4 = 0
=> x2 – 3x + 2 = 0
[Dividing each term by 2]
=> x2 – 2x – x + 2 = 0
=> x(x – 2) (x – 1) = 0
=> x – 2 = 0        or x – 1 = 0
=> x = 2             or x = 1
∴ The other (second) root is 1.
 
Q.- In the following, find the value (s) of p so that the given equation has equal roots.
(i) 3x2– 5x + p = 0
(ii) 2px2 – 8x + p = 0

Sol. (i) Comparing 3x2 – 5x + p = 0

with ax2 + bx + c = 0,

we get : a = 3, b = – 5 and c = p
Since, the roots are equal ; the discriminant
b2 – 4ac = 0
i.e., (–5)2 – 4 × 3 × p = 0
=> 25 – 12p = 0 and p = 25/12  = 2 1/12
 
(ii) Comparing 2px2 – 8x + p = 0
with ax2 + bx + c = 0;
we get : a = 2p, b = – 8 and c = p
b2 – 4ac = 0 [Given, that the roots are equal]
=> (–8)2 – 4 × 2p × p = 0
=> 64 – 8p2 = 0
=> – 8p2 = – 64, p2 = 8 and p = ± √8
i.e., p = ± 2√ 2
 
Q.- If α and β are the roots of the quadratic equation ax2 + bx + c = 0, (a ≠ 0) then find the values of :
(i) α2 + β2
(ii) α3 + β3
(iii)α /β + β/α
 

Quadratic equations notes 1

Quadratic equations notes 2

Q.- Solve the following equations :
(i) x4 – 26x2 + 25 = 0
(ii) z4 – 10z2 + 9 = 0
 
Sol. (i) Substituting x2 = y :
x4 – 26x2 + 25 = 0
=> y2 – 26y + 25 = 0
i.e., y2 – 25y – y + 25 = 0
=> y(y – 25) – 1(y – 25) = 0
i.e., (y – 25) (y – 1) = 0
=> y – 25 = 0 or y – 1 = 0
i.e., y = 25 or y = 1
y = 25 => x2 = 25 | y = 1
=> x2 = 1
=> x = ± 5 |
=> x = ± 1
∴Roots of the given equation are : ± 5, ± 1

 

Please click the link below to download CBSE Class 10 Mathematics Quadratic Equation Worksheet Set D

Chapter 01 Real Numbers
CBSE Class 10 Mathematics Real Numbers Worksheet Set A
CBSE Class 10 Mathematics Real Numbers Worksheet Set B
CBSE Class 10 Mathematics Real Numbers Worksheet Set C
CBSE Class 10 Mathematics Real Numbers Worksheet Set D
CBSE Class 10 Mathematics Real Numbers Worksheet Set E
CBSE Class 10 Mathematics Real Numbers Worksheet Set F
CBSE Class 10 Mathematics Real Numbers Worksheet Set G
Chapter 02 Polynomials
CBSE Class 10 Mathematics Polynomials Worksheet Set A
CBSE Class 10 Mathematics Polynomials Worksheet Set B
CBSE Class 10 Mathematics Polynomials Worksheet Set C
CBSE Class 10 Mathematics Polynomials Worksheet Set D
CBSE Class 10 Mathematics Polynomials Worksheet Set E
CBSE Class 10 Mathematics Polynomials Worksheet Set F
CBSE Class 10 Mathematics Polynomials Worksheet Set G
CBSE Class 10 Mathematics Polynomials Worksheet Set H
CBSE Class 10 Mathematics Polynomials Worksheet Set I
CBSE Class 10 Mathematics Polynomials Worksheet Set J
CBSE Class 10 Mathematics Polynomials Worksheet Set K
Chapter 03 Pair of Linear Equations in Two Variables
CBSE Class 10 Mathematics Pair Of Linear Equations In 2 Variables Worksheet Set A
CBSE Class 10 Mathematics Pair Of Linear Equations In 2 Variables Worksheet Set B
CBSE Class 10 Mathematics Pair Of Linear Equations In 2 Variables Worksheet Set C
CBSE Class 10 Mathematics Pair Of Linear Equations In 2 Variables Worksheet Set D
CBSE Class 10 Mathematics Pair Of Linear Equations In 2 Variables Worksheet Set E
CBSE Class 10 Mathematics Pair Of Linear Equations In 2 Variables Worksheet Set F
Chapter 04 Quadratic Equation
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set A
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set C
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set D
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set E
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set F
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set I
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set J
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set K
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set L
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set M
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set N
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set O
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set P
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set Q
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set R
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set S
Chapter 05 Arithmetic Progression
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set A
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set B
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set C
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set D
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set E
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set F
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set G
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set H
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set I
Chapter 06 Triangles
CBSE Class 10 Mathematics Triangles Worksheet Set A
CBSE Class 10 Mathematics Triangles Worksheet Set B
CBSE Class 10 Mathematics Triangles Worksheet Set C
CBSE Class 10 Mathematics Triangles Worksheet Set D
CBSE Class 10 Mathematics Triangles Worksheet Set E
CBSE Class 10 Mathematics Triangles Worksheet Set F
CBSE Class 10 Mathematics Triangles Worksheet Set G
CBSE Class 10 Mathematics Triangles Worksheet Set H
Chapter 07 Coordinate Geometry
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set A
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set B
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set C
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set D
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set E
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set F
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set G
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set H
Chapter 08 Introduction to Trigonometry
CBSE Class 10 Mathematics Introduction to Trigonometry Worksheet Set A
CBSE Class 10 Mathematics Introduction to Trigonometry Worksheet Set B
Chapter 09 Some Applications of Trigonometry
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set A
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set B
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set C
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set D
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set E
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set F
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set G
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set H
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set I
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set J
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set K
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set L
Chapter 10 Circles
CBSE Class 10 Mathematics Circles Worksheet Set A
CBSE Class 10 Mathematics Circles Worksheet Set B
CBSE Class 10 Mathematics Circles Worksheet Set C
CBSE Class 10 Mathematics Circles Worksheet Set D
CBSE Class 10 Mathematics Circles Worksheet Set E
CBSE Class 10 Mathematics Circles Worksheet Set F
CBSE Class 10 Mathematics Circles Worksheet Set G
CBSE Class 10 Mathematics Circles Worksheet Set H
Chapter 11 Areas related to Circles
CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set A
CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set B
CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set C
CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set D
CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set E
CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set F
CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set G
Chapter 12 Surface Areas and Volumes
CBSE Class 10 Mathematics Surface Areas and Volumes Worksheet Set A
CBSE Class 10 Mathematics Surface Areas and Volumes Worksheet Set B
CBSE Class 10 Mathematics Surface Areas and Volumes Worksheet Set C
Chapter 13 Statistics
CBSE Class 10 Mathematics Statistics Worksheet Set A
CBSE Class 10 Mathematics Statistics Worksheet Set B
CBSE Class 10 Mathematics Statistics Worksheet Set C
CBSE Class 10 Mathematics Statistics Worksheet Set D
CBSE Class 10 Mathematics Statistics Worksheet Set E
CBSE Class 10 Mathematics Statistics Worksheet Set F
CBSE Class 10 Mathematics Statistics Worksheet Set G
CBSE Class 10 Mathematics Statistics Worksheet Set H
CBSE Class 10 Mathematics Statistics Worksheet Set I
CBSE Class 10 Mathematics Statistics Worksheet Set J
Chapter 14 Probability
CBSE Class 10 Mathematics Probability Worksheet Set A
CBSE Class 10 Mathematics Probability Worksheet Set B
CBSE Class 10 Mathematics Probability Worksheet Set C
Other Topics
Case Study Chapter 1 Real Numbers Mathematics
Case Study Chapter 2 Polynomials Mathematics
Case Study Chapter 3 Linear Equations Mathematics
Case Study Chapter 6 Triangles Mathematics
Case Study Chapter 7 Coordinate Geometry Mathematics
Case Study Chapter 8 Trigonometry Mathematics
Case Study Chapter 11 Areas related to Circles Mathematics
Case Study Chapter 14 Probability Mathematics
CBSE Class 10 Mathematics Number Systems Worksheet

Important Practice Resources for Class 10 Mathematics

CBSE Mathematics Class 10 Chapter 4 Quadratic Equation Worksheet

Students can use the practice questions and answers provided above for Chapter 4 Quadratic Equation to prepare for their upcoming school tests. This resource is designed by expert teachers as per the latest 2026 syllabus released by CBSE for Class 10. We suggest that Class 10 students solve these questions daily for a strong foundation in Mathematics.

Chapter 4 Quadratic Equation Solutions & NCERT Alignment

Our expert teachers have referred to the latest NCERT book for Class 10 Mathematics to create these exercises. After solving the questions you should compare your answers with our detailed solutions as they have been designed by expert teachers. You will understand the correct way to write answers for the CBSE exams. You can also see above MCQ questions for Mathematics to cover every important topic in the chapter.

Class 10 Exam Preparation Strategy

Regular practice of this Class 10 Mathematics study material helps you to be familiar with the most regularly asked exam topics. If you find any topic in Chapter 4 Quadratic Equation difficult then you can refer to our NCERT solutions for Class 10 Mathematics. All revision sheets and printable assignments on studiestoday.com are free and updated to help students get better scores in their school examinations.

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