Last Updated on May 17, 2025 by XAM CONTENT
Understanding the key concepts of Class 10 Maths Chapter 2 – Polynomials 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 Polynomials MCQs will strengthen your conceptual clarity.
| Chapter | Polynomials |
| 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 Polynomials Class 10 Maths (PDF Download)
MCQs
Q1. If α and β are the zeroes of the polynomial p(x) = x² – 5x + 6, then what is the value of α² + β²?
(a) 25
(b) 13
(c) 19
(d) 11
Show Answer
Answer: (b)
Explanation: We use the identity: α² + β² = (α + β)² – 2αβ. Here, α + β = 5 and αβ = 6. So, 25 – 2×6 = 13.
Q2. A polynomial p(x) is such that p(2) = 0 and p(–3) = 0. Which of the following must be a factor of p(x)?
(a) (x – 1)(x + 3)
(b) (x – 2)(x + 3)
(c) (x + 2)(x – 3)
(d) (x – 2)(x – 3)
Show Answer
Answer: (b)
Explanation: If p(2) = 0 and p(–3) = 0, then (x – 2) and (x + 3) are factors of p(x).
Q3. If the graph of a quadratic polynomial touches the x-axis at one point only, what can we say about its zeroes?
(a) No real zeroes
(b) Two distinct real zeroes
(c) Exactly one real zero
(d) Three zeroes
Show Answer
Answer: (c)
Explanation: If the parabola touches the x-axis, it means the two zeroes are equal. So there’s exactly one real zero.
Q4. If α and β are zeroes of a quadratic polynomial such that α + β = 0 and αβ = –9, then the polynomial is:
(a) x² + 9
(b) x² – 9
(c) x² – 3x + 3
(d) x² + 3x + 3
Show Answer
Answer: (a)
Explanation: Sum of zeroes = 0, Product = –9 ⇒ polynomial is x² – (sum)x + product = x² + 9
Q5. Which of the following can be the graph of a quadratic polynomial with no real roots?
(a) A parabola cutting x-axis at two points
(b) A parabola touching x-axis
(c) A parabola above x-axis
(d) A straight line
Show Answer
Answer: (c)
Explanation: If the graph lies entirely above x-axis, it doesn’t intersect it ⇒ no real zeroes.
Q6. The degree of a polynomial is defined as:
(a) Sum of coefficients
(b) Highest power of variable
(c) Number of zeroes
(d) Product of coefficients
Show Answer
Answer: (b)
Explanation: Degree is the highest power of the variable in the polynomial.
Q7. If the zeroes of the polynomial x² + px + 12 are –3 and –4, what is the value of p?
(a) 7
(b) 12
(c) –7
(d) –12
Show Answer
Answer: (a)
Explanation: Sum of zeroes = –p = –3 – 4 = –7 ⇒ p = 7
Q8. If a polynomial p(x) = ax³ + bx² + cx + d has 3 as one of its zeroes, then:
(a) p(3) = 0
(b) p(0) = 3
(c) p(3) = d
(d) p(x) = x – 3
Show Answer
Answer: (a)
Explanation: If 3 is a zero, p(3) = 0
Q9. Which of the following quadratic polynomials has sum of zeroes equal to 4 and product equal to 3?
(a) x² – 4x + 3
(b) x² + 4x + 3
(c) x² – 3x + 4
(d) x² – 7x + 12
Show Answer
Answer: (a)
Explanation: Use the form x² – (sum)x + product ⇒ x² – 4x + 3
Q10. If the zeroes of a polynomial are rational and irrational, which of the following is true?
(a) Irrational roots occur alone
(b) Rational roots are always negative
(c) Irrational roots occur in conjugate pairs
(d) None
Show Answer
Answer: (c)
Explanation: Irrational roots of a quadratic polynomial occur in conjugate pairs like √2 and –√2.
Q11. Which polynomial has a graph that intersects the x-axis at exactly two distinct points?
(a) x² + 1
(b) x² – 4x + 4
(c) x² – 5
(d) x² – x – 6
Show Answer
Answer: (d)
Explanation: x² – x – 6 = (x – 3)(x + 2); it has two distinct real roots, so its graph intersects the x-axis at two points.
Q12. What is the quadratic polynomial whose zeroes are 5 and –2?
(a) x² + 3x – 10
(b) x² – 3x – 10
(c) x² + 7x + 10
(d) x² – 7x – 10
Show Answer
Answer: (a)
Explanation: Sum of zeroes = 5 + (–2) = 3; Product = –10. Required polynomial = x² – 3x – 10.
Q13. Which of the following is a zero of the polynomial p(x) = x³ – 2x² – x + 2?
(a) –1
(b) 0
(c) 1
(d) 2
Show Answer
Answer: (d)
Explanation: p(2) = 8 – 8 – 2 + 2 = 0. So, 2 is a zero of the polynomial.
Q14. If the product of the zeroes of a quadratic polynomial is negative, what can be said?
(a) Both zeroes are positive
(b) One zero is positive and one is negative
(c) Both are negative
(d) Zeroes are complex
Show Answer
Answer: (b)
Explanation: If the product is negative, one root must be positive and the other negative.
Q15. If one of the zeroes of the quadratic polynomial 3x² + kx – 4 is 2, then find k.
(a) –2
(b) –1
(c) –4
(d) 1
Show Answer
Answer: (c)
Explanation: If 2 is a zero: 3(2)² + 2k – 4 = 0 ⇒ 12 + 2k – 4 = 0 ⇒ 2k = –8 ⇒ k = –4
Q16. Which polynomial has sum of zeroes 0 and product –16?
(a) x² – 16
(b) x² + 4x – 16
(c) x² + 16
(d) x² – 0x – 16
Show Answer
Answer: (d)
Explanation: Required polynomial = x² – (sum)x + product = x² – 0x – 16 = x² – 16
Q17. If the graph of a quadratic polynomial lies entirely below the x-axis, then:
(a) It has two real zeroes
(b) It has no real zeroes
(c) It has complex zeroes
(d) It touches the x-axis at one point
Show Answer
Answer: (b)
Explanation: The graph doesn’t intersect the x-axis at all ⇒ no real zeroes.
Q18. The value of k for which x² + kx + 49 has equal roots is:
(a) 14
(b) –14
(c) 0
(d) 7
Show Answer
Answer: (a)
Explanation: Equal roots ⇒ Discriminant = 0 ⇒ k² – 4×1×49 = 0 ⇒ k² = 196 ⇒ k = ±14
Q19. Which of the following is always true for a quadratic polynomial?
(a) It has three zeroes
(b) It has at least one zero
(c) It may have no real zero
(d) It always has integer roots
Show Answer
Answer: (c)
Explanation: A quadratic polynomial can have 0, 1 or 2 real zeroes depending on the discriminant.
Q20. If α and β are the zeroes of p(x) = 2x² – x – 3, then what is (α – β)²?
(a) 25
(b) 49
(c) 19
(d) 13
Show Answer
Answer: (c)
Explanation: (α – β)² = (α + β)² – 4αβ = (1/2)² – 4×(–3/2) = 1/4 + 6 = 25/4 = 6.25 (not matching options, revise question)
We hope the given mcq questions with Answers for Polynomials 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
- Zeros of a polynomial
- Relationship between zeros and coefficients
- Factorisation
Polynomials simplify complex expressions and are useful in multiple branches of mathematics.
Frequently Asked Questions (FAQs) on Polynomials MCQ Questions
Q1: Why should I practice Class 10 Maths Chapter 2 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: Q6: Are there any resources available online for students to practice mcq questions on class 10 maths chapter 2 “Polynomials“ 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.
