CBSE Class 10 Mathematics (Standard) Chapter 2 Polynomials Important Questions 2027
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16 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 2.3 questions per paper (OR alternatives counted separately)
- 5 question patterns repeated across papers
Important topics in Polynomials
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Relationship between zeros and coefficients (quadratic) | Board 2023Board 2024Board 2025Board 2026Sample 2026 | ★★☆☆☆ |
| 2 | Zeros of a polynomial from graph | Board 2023Board 2024Board 2025Board 2026Sample 2025 | ★☆☆☆☆ |
| 3 | Forming a quadratic polynomial from given zeros | Board 2023Sample 2025 | ★☆☆☆☆ |
Repeated questions from Polynomials
1. Find unknown coefficient from condition on zeroes
3×Board 2024Board 2025Board 20261 marks
If alpha and beta are two zeroes of a polynomial f(x) = px2 - 2x + 3p and alpha + beta = alpha*beta, then value of p is : (A) -2/3 (B) 2/3 (C) 1/3 (D) -1/3
2. Count zeroes from graph
3×Board 2023Board 2025Board 20261 marks
The graph of y = f(x) is given. The number of distinct zeroes of y = f(x) is : (A) 0 (B) 1 (C) 2 (D) 3 [Figure: curve crossing x-axis at A and touching it at another point]
3. Find zeroes by factorisation (and verify)
2×Board 2025Sample 20262/3 marks
Find the zeroes of the quadratic polynomial 2x2 - (1 + 2*sqrt(2))x + sqrt(2) and verify the relationship between the zeroes and coefficients of the polynomial.
4. Identify quadratic with given plus/minus zeroes
2×Board 2023Sample 20251 marks
A quadratic polynomial having zeroes -sqrt(5/2) and sqrt(5/2) is A) x2 - 5*sqrt(2)x + 1 B) 8x2 - 20 C) 15x2 - 6 D) x2 - 2*sqrt(5)x - 1
5. Evaluate symmetric expression in zeroes
2×Board 2023Board 20261/2 marks
If alpha, beta are the zeroes of the quadratic polynomial px2 + qx + r, then find the value of alpha3 * beta + beta3 * alpha.
Polynomials questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 0 | 0 |
| Board 2023 | 3 | 3 |
| Board 2024 | 3 | 3 |
| Board 2025 | 3 | 4 |
| Sample 2025 | 3 | 5 |
| Board 2026 | 3 | 4 |
| Sample 2026 | 1 | 3 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Polynomials
Board 2026 3 questions
The graph of y = f(x) is given. The number of distinct zeroes of y = f(x) is : (A) 0 (B) 1 (C) 2 (D) 3 [Figure: curve crossing x-axis at A and touching it at another point]
If alpha and beta are two zeroes of a polynomial f(x) = px2 - 2x + 3p and alpha + beta = alpha*beta, then value of p is : (A) -2/3 (B) 2/3 (C) 1/3 (D) -1/3
If alpha, beta are the zeroes of the quadratic polynomial px2 + qx + r, then find the value of alpha3 * beta + beta3 * alpha.
Sample 2026 1 question
Find the zeroes of the quadratic polynomial 2x2 - (1 + 2*sqrt(2))x + sqrt(2) and verify the relationship between the zeroes and coefficients of the polynomial.
Board 2025 3 questions
If alpha and beta are the zeroes of polynomial 3x2 + 6x + k such that alpha + beta + alpha*beta = -2/3, then the value of k is : (A) -8 (B) 8 (C) -4 (D) 4
Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is : [graph shows an upward parabola and a downward parabola intersecting the x-axis at the same two points] (A) 3 (B) 5 (C) 2 (D) 4
Find the zeroes of the polynomial p(x) = x2 + (4/3)x - 4/3.
Sample 2025 3 questions
The graph of a quadratic polynomial p(x) passes through the points (-6,0), (0, -30), (4,-20) and (6,0). The zeroes of the polynomial are A) -6,0 B) 4,6 C) -30,-20 D) -6,6
A quadratic polynomial having zeroes -sqrt(5/2) and sqrt(5/2) is A) x2 - 5*sqrt(2)x + 1 B) 8x2 - 20 C) 15x2 - 6 D) x2 - 2*sqrt(5)x - 1
If alpha and beta are zeroes of a polynomial 6x2 - 5x + 1 then form a quadratic polynomial whose zeroes are alpha2 and beta2.
Board 2024 3 questions
If the sum of zeroes of the polynomial p(x) = 2x2 - k*sqrt(2)x + 1 is sqrt(2), then value of k is: (a) sqrt(2) (b) 2 (c) 2*sqrt(2) (d) 1/2
The zeroes of a polynomial x2 + px + q are twice the zeroes of the polynomial 4x2 - 5x - 6. The value of p is: (a) -5/2 (b) 5/2 (c) -5 (d) 10
Assertion (A): If the graph of a polynomial touches x-axis at only one point, then the polynomial cannot be a quadratic polynomial. Reason (R): A polynomial of degree n (n > 1) can have at most n zeroes. Choose the correct option: (a) Both A and R are true and R is correct explanation of A. (b) Both A and R are true but R is not correct explanation of 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 given, for a polynomial p(x). The number of zeroes of p(x) from the graph is [parabola opening downward touching x-axis at one point near origin] (A) 3 (B) 1 (C) 2 (D) 0
If alpha, beta are the zeroes of a polynomial p(x) = x2 + x - 1, then 1/alpha + 1/beta equals to (A) 1 (B) 2 (C) -1 (D) -1/2
Which of the following is a quadratic polynomial having zeroes -2/3 and 2/3? (A) 4x2 - 9 (B) 4/9 (9x2 + 4) (C) x2 + 9/4 (D) 5(9x2 - 4)
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Standard) Chapter 2 Polynomials?
By how often and how recently they were asked: Relationship between zeros and coefficients (quadratic); Zeros of a polynomial from graph; Forming a quadratic polynomial from given zeros.
How many marks does Polynomials carry in the CBSE Class 10 Mathematics (Standard) exam?
Polynomials is part of the Algebra unit, which carries 20 marks in the official syllabus. In the analysed papers it had about 2.3 questions per paper.
Do questions from Polynomials repeat in board exams?
Yes — 5 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.