Understanding the key concepts of Class 10 Maths Chapter 4 – Quadratic Equations is crucial for exam success. To make your revision easier, we have created chapterwise mcq questions with Answers for class 10 Maths based on the latest syllabus and exam pattern. It is a part of MCQ Questions for CBSE Class 10 Maths Series.
These multiple-choice questions will help you assess your knowledge, improve accuracy, and boost confidence for your exams. Whether you are preparing for school tests, online tests or competitive exams, these Quadratic Equations MCQs will strengthen your conceptual clarity.
| Chapter | Quadratic Equations |
| Book | Maths Textbook for Class 10 |
| Type of Questions | MCQ Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 10 |
| Subject | Maths |
| Useful for | Class 10 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 10 Maths Chapterwise MCQ Questions |
MCQ Questions on Quadratic Equations Class 10 Maths (PDF Download)
MCQs
Q1. Which of the following quadratic equations has no real roots?
(a) x² – 2x + 1 = 0
(b) x² + 2x + 3 = 0
(c) x² – 3x + 2 = 0
(d) 2x² – 4x + 2 = 0
Show Answer
Answer: (b)
Explanation: Discriminant D = b² – 4ac = 4 – 12 = –8 < 0 ⇒ no real roots.
Q2. If one root of the quadratic equation ax² + bx + c = 0 is twice the other, then the condition among coefficients is:
(a) b² = 9ac
(b) b² = 4ac
(c) 2b² = 9ac
(d) b² = 8ac
Show Answer
Answer: (d)
Explanation: Let roots be α and 2α. Then α + 2α = –b/a, α·2α = c/a ⇒ solve to get b² = 8ac.
Q3. What is the sum of roots of the quadratic equation 3x² – 5x + 2 = 0?
(a) –5
(b) 5/3
(c) –2/3
(d) 5
Show Answer
Answer: (b)
Explanation: Sum = –b/a = –(–5)/3 = 5/3.
Q4. If the roots of the quadratic equation are real and equal, then the graph of the equation will:
(a) Touch the x-axis
(b) Intersect the x-axis
(c) Never touch x-axis
(d) Be a straight line
Show Answer
Answer: (a)
Explanation: Equal roots ⇒ parabola touches x-axis at one point.
Q5. If a quadratic equation has two real roots, which of the following must be true?
(a) Discriminant = 0
(b) Discriminant > 0
(c) Discriminant ≥ 0
(d) Discriminant < 0
Show Answer
Answer: (c)
Explanation: Two real roots possible when discriminant is ≥ 0.
Q6. If the equation x² – (k + 1)x + k = 0 has equal roots, then k is:
(a) 0
(b) 1
(c) –1
(d) 2
Show Answer
Answer: (b)
Explanation: Equal roots ⇒ D = 0 ⇒ (k + 1)² – 4k = 0 ⇒ k = 1.
Q7. The quadratic equation whose roots are reciprocals of the roots of 2x² + 3x + 5 = 0 is:
(a) 5x² + 3x + 2 = 0
(b) 2x² + 5x + 3 = 0
(c) 3x² + 2x + 5 = 0
(d) 5x² + 2x + 3 = 0
Show Answer
Answer: (a)
Explanation: Required equation = 5x² + 3x + 2 = 0
Q8. If one root of the equation x² + px + 12 = 0 is 4, the other is:
(a) 3
(b) –3
(c) –4
(d) –1
Show Answer
Answer: (b)
Explanation: Product of roots = 12 ⇒ 4·other = 12 ⇒ other = 3 ⇒ sum = –p ⇒ p = –7
Q9. What is the condition for a quadratic equation to have complex roots?
(a) b² – 4ac = 0
(b) b² – 4ac > 0
(c) b² – 4ac < 0
(d) b² = 4ac
Show Answer
Answer: (c)
Explanation: If discriminant is negative, the roots are complex conjugates.
Q10. Which of the following equations has irrational roots?
(a) x² – 6x + 9 = 0
(b) x² – 2x – 1 = 0
(c) x² + 2x + 1 = 0
(d) x² – 4x + 4 = 0
Show Answer
Answer: (b)
Explanation: Discriminant = 2² + 4 = 8 ⇒ not a perfect square ⇒ irrational roots.
Q11. What is the quadratic equation whose roots are squares of the roots of x² – 3x + 2 = 0?
(a) x² – 6x + 9 = 0
(b) x² – 5x + 6 = 0
(c) x² – 10x + 21 = 0
(d) x² – 7x + 12 = 0
Show Answer
Answer: (c)
Explanation: Original roots: 1 and 2 ⇒ squares: 1 and 4 ⇒ new roots ⇒ sum = 5, product = 4 ⇒ x² – 5x + 4
Q12. If one root of the quadratic equation is the square of the other and the sum of the roots is 5, find the equation.
(a) x² – 6x + 9 = 0
(b) x² – 5x + 6 = 0
(c) x² – 7x + 12 = 0
(d) x² – 10x + 25 = 0
Show Answer
Answer: (d)
Explanation: Let roots be a and a². Then a + a² = 5 ⇒ a² + a – 5 = 0 ⇒ solve for a, get roots.
Q13. If x = –1 is a root of the quadratic equation ax² + bx + c = 0 and a + b + c = 0, then:
(a) a = 0
(b) b = 0
(c) c = 0
(d) None of these
Show Answer
Answer: (d)
Explanation: Substitute x = –1 ⇒ a – b + c = 0. Use a + b + c = 0 ⇒ solve equations.
Q14. If the roots of ax² + bx + c = 0 are equal, then the vertex of the parabola lies:
(a) On the x-axis
(b) Above the x-axis
(c) Below the x-axis
(d) On the line y = 1
Show Answer
Answer: (a)
Explanation: Equal roots ⇒ vertex lies on the x-axis ⇒ y = 0
Q15. The sum and product of the roots of a quadratic equation are equal. Which of the following could be the equation?
(a) x² – 4x + 4 = 0
(b) x² – 2x + 1 = 0
(c) x² – 2x + 2 = 0
(d) x² – x + 1 = 0
Show Answer
Answer: (b)
Explanation: Sum = 2, product = 1 ⇒ sum ≠ product for most ⇒ check for equality ⇒ only (b) works
Q16. The roots of a quadratic equation are imaginary when the discriminant is:
(a) Greater than 0
(b) Equal to 0
(c) Less than 0
(d) Equal to 1
Show Answer
Answer: (c)
Explanation: Imaginary roots occur when D < 0.
Q17. If the equation x² + kx + 16 = 0 has real and equal roots, what is the value of k?
(a) 8
(b) –8
(c) 4
(d) –4
Show Answer
Answer: (b)
Explanation: Equal roots ⇒ D = 0 ⇒ k² – 64 = 0 ⇒ k = ±8
Q18. Which of the following represents a quadratic equation with roots –1 and –2?
(a) x² + 3x + 2 = 0
(b) x² – 3x + 2 = 0
(c) x² + x + 2 = 0
(d) x² – x – 2 = 0
Show Answer
Answer: (a)
Explanation: Sum = –3, product = 2 ⇒ x² + 3x + 2 = 0
Q19. What is the maximum number of real roots a quadratic equation can have?
(a) 1
(b) 2
(c) 3
(d) Infinite
Show Answer
Answer: (b)
Explanation: Quadratic equations have at most 2 real roots.
Q20. A quadratic equation has one root as 0.5. What could be the other root if the product of the roots is 1?
(a) 2
(b) 1
(c) 0.5
(d) None
Show Answer
Answer: (a)
Explanation: Product = 0.5 × other = 1 ⇒ other = 2
We hope the given mcq questions with Answers for Quadratic Equations Class 10 helps you in your learning.
Also check
- Arithmetic Progressions – Class 10 Maths Chapter 5 MCQ Questions with Answers (Updated)
- Quadratic Equations – Class 10 Maths Chapter 4 MCQ Questions with Answers (Updated)
- Pair of Linear Equations in Two Variables – Class 10 Maths Chapter 3 MCQ Questions with Answers (Updated)
- Polynomials – Class 10 Maths Chapter 2 MCQ Questions with Answers (Updated)
- Real Numbers – Class 10 Maths Chapter 1 MCQ Questions with Answers (Updated)
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Topics from which mcq questions may be asked
- Roots of quadratic equations
- Factorisation and formula methods
- Discriminant
Quadratic equations arise naturally in many practical situations from physics to finance.
Frequently Asked Questions (FAQs) on Quadratic Equations MCQ Questions
Q1: Why should I practice Class 10 Maths Chapter 4 MCQs?
A1: Practicing MCQs helps in quick revision, improves problem-solving speed, and enhances conceptual understanding of important topics in Class 6 Maths.
Q2: Are these Class 10 Maths MCQs based on the latest syllabus?
A2: Yes, all the MCQs are designed as per the latest CBSE syllabus and exam pattern to help students prepare effectively.
Q3: Where can I find more MCQs for Class 10 Maths?
A3: You can find more chapter-wise MCQs on our website. These are designed to cover important concepts and prepare you for exams.
Q4: Are the answers provided for all MCQs?
A4: Yes, each MCQ is accompanied by the correct answer and explanations to help students understand and learn better.
Q5: How can I improve my performance in Class 10 Maths MCQs?
A5: To improve your performance, practice regularly, revise key concepts, and take mock tests to assess your knowledge.
Q6: Do these MCQs help in school exams?
A6: Yes, these MCQs are aligned with school exam patterns and help in scoring well by strengthening conceptual clarity.
Q7: Can I download these MCQs for offline practice?
A7: Yes, you can download or print these MCQs for convenient offline practice.
Q8: Are there any resources available online for students to practice mcq questions on class 10 maths chapter 4 “Quadratic Equations“ for CBSE exams?
A6: Yes, several educational websites offer mcq questions for CBSE students preparing for maths examinations. We also offer a collection of mcq questions for all classes and subject on our website. Visit our website to access these questions and enhance your learning experience. for more mcq, you can also visit Physics Gurukul Website.
