CBSE Class 10 Mathematics (Basic) Chapter 2 Polynomials Important Questions 2027
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15 questions from Polynomials appeared in 6 of the 7 CBSE papers we analysed (2022–2026) — here are the topics that matter, the questions that repeat, and every previous-year question from this chapter.
Key facts
- Algebra unit — 20 marks in the official syllabus
- Asked in 6 of 7 analysed papers (2022–2026)
- About 2.1 questions per paper (OR alternatives counted separately)
- 1 question patterns repeated across papers
Important topics in Polynomials
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Zeros of a polynomial from graph | Board 2023Board 2024Sample 2025 | ★★☆☆☆ |
| 2 | Forming a quadratic polynomial from given zeros | Board 2023Board 2025Board 2026Sample 2025Sample 2026 | ★☆☆☆☆ |
| 3 | Relationship between zeros and coefficients (quadratic) | Board 2023Board 2024Sample 2026 | ★☆☆☆☆ |
Repeated questions from Polynomials
1. Form quadratic polynomial from zeroes or sum and product
3×Board 2025Board 2026Sample 20251/3 marks
Find a quadratic polynomial whose sum and product of zeroes are 0 and – 9, respectively. Also, find the zeroes of the polynomial so obtained.
Polynomials questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 0 | 0 |
| Board 2023 | 3 | 5 |
| Board 2024 | 3 | 3 |
| Board 2025 | 1 | 3 |
| Sample 2025 | 5 | 7 |
| Board 2026 | 1 | 3 |
| Sample 2026 | 2 | 3 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Polynomials
Board 2026 1 question
Find a quadratic polynomial whose sum and product of zeroes are 0 and – 9, respectively. Also, find the zeroes of the polynomial so obtained.
Sample 2026 2 questions
The number of polynomials having −2 and 5 as its zeroes is
A) one
B) two
C) three
D) Infinitely many
If the zeroes of the quadratic polynomial x2 + (a + 1)x + b are 2 and −3, then find the values of a and b.
Board 2025 1 question
Find a quadratic polynomial whose sum and product of zeroes are 0 and -9, respectively. Also, find the zeroes of the polynomial so obtained.
Sample 2025 5 questions
A quadratic polynomial whose zeroes are 2/5 and −1/5 is (A) 25x2 + 5x − 2 (B) 5x2 − 2x + 1 (C) 5x2 + 2x − 1 (D) 25x2 − 5x − 2
[Case study: Water fountains form a parabola; the downward-facing parabola representing the water fountain is p(x) = −x2 + 5x − 4, shown on the given graph. Height of each fountain rod above water level is 10 cm.] Find the zeroes of the polynomial p(x) from the graph.
[Case study: Water fountains form a parabola; the downward-facing parabola representing the water fountain is p(x) = −x2 + 5x − 4, shown on the given graph. Height of each fountain rod above water level is 10 cm.] Find the value of x at which water attains maximum height.
[Case study: Water fountains form a parabola; the downward-facing parabola representing the water fountain is p(x) = −x2 + 5x − 4, shown on the given graph. Height of each fountain rod above water level is 10 cm.] If h is the maximum height attained by the water stream from the water level of the pool, then find the value of h.
[Case study: Water fountains form a parabola; the downward-facing parabola representing the water fountain is p(x) = −x2 + 5x − 4, shown on the given graph. Height of each fountain rod above water level is 10 cm.] At what point(s) on x-axis, the height of water above x-axis is 2 m?
Board 2024 3 questions
For what value of k, the product of zeroes of the polynomial kx2 - 4x - 7 is 2 ? (a) -1/14 (b) -7/2 (c) 7/2 (d) -2/7
If one of the zeroes of the quadratic polynomial (α-1)x2 + αx + 1 is -3, then the value of α is : (a) -2/3 (b) 2/3 (c) 4/3 (d) 3/4
Assertion (A): Zeroes of a polynomial p(x) = x2 - 2x - 3 are -1 and 3. Reason (R): The graph of polynomial p(x) = x2 - 2x - 3 intersects x-axis at (-1, 0) and (3, 0). Options: (a) Both A and R are true and R explains A completely. (b) Both A and R are true but R does not explain A. (c) A is true but R is false. (d) A is false but R is true.
Board 2023 3 questions
The graph of y = p(x) is shown in the figure for some polynomial p(x). The number of zeroes of p(x) is/are : (a) 0 (b) 1 (c) 2 (d) 3
The sum and the product of zeroes of the polynomial p(x) = x2 + 5x + 6 are respectively : (a) 5, − 6 (b) − 5, 6 (c) 2, 3 (d) −2, −3
If α, β are zeroes of the quadratic polynomial x2 + 3x + 2, find a quadratic polynomial whose zeroes are α + 1, β + 1.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Basic) Chapter 2 Polynomials?
By how often and how recently they were asked: Zeros of a polynomial from graph; Forming a quadratic polynomial from given zeros; Relationship between zeros and coefficients (quadratic).
How many marks does Polynomials carry in the CBSE Class 10 Mathematics (Basic) exam?
Polynomials is part of the Algebra unit, which carries 20 marks in the official syllabus. In the analysed papers it had about 2.1 questions per paper.
Do questions from Polynomials repeat in board exams?
Yes — 1 question patterns from this chapter appeared in two or more past board or official sample papers. They are listed on this page with the years they were asked.