THE GOAL • CBSE CLASS 10

POLYNOMIALS

Chapter 2 • Basic Mathematics • 2025 PYQs

CBSE 2025 Basic Mathematics Previous Year Questions Chapter-wise Collection

Chapter 2: Polynomials

Unique Previous Year Questions extracted from the CBSE Class 10 Basic Mathematics 2025 question paper sets. Redundant questions have been removed while retaining the major question types and variations.

I

Multiple Choice Questions

1. Graph Based – Zeroes
1 Mark
In the given figure, the graph of polynomial \(p(x)\) is shown. The number of zeroes of \(p(x)\) is:
(A) 3
(B) 2
(C) 1
(D) 4
Set 430/6/1
2. Evaluating Expressions in \(\alpha,\beta\)
1 Mark
If \(\alpha,\beta\) are zeroes of the polynomial \[ 2x^2+5x+1, \] then the value of \[ \frac{1}{\alpha}+\frac{1}{\beta} \] is:
(A) \(-\frac{5}{4}\)
(B) \(5\)
(C) \(\frac{5}{4}\)
(D) \(-5\)
Set 430/4/2
3. Evaluating Sum / Product of Zeroes
1 Mark
If \(\alpha,\beta\) are zeroes of the polynomial \[ 3x^2+14x-5, \] then the value of \[ 3\left(\frac{\alpha+\beta}{\alpha\beta}\right) \] is:
(A) \(\frac{14}{5}\)
(B) \(\frac{42}{5}\)
(C) \(-\frac{14}{5}\)
(D) \(-\frac{42}{5}\)
Set 430/4/3
4. Identifying Polynomial
1 Mark
A quadratic polynomial having only one zero \((-2)\) is:
(A) \((x-2)^2\)
(B) \(x^2-2\)
(C) \(x^2+2x\)
(D) \((x+2)^2\)
Set 430/5/1
5. Graph Interpretation – Distinct Zeroes
1 Mark
Observe the given graph of polynomial \(p(x)\). The number of distinct zeroes of \(p(x)\) is:
(A) 0
(B) 1
(C) 2
(D) many
Set 430/4/2
II

Assertion – Reason Question

6. Quadratic Polynomial and Real Roots
1 Mark
Assertion (A): Every quadratic equation has two real roots.
Reason (R): A quadratic polynomial can have at most two zeroes.
Set 430/3/1
III

Short Answer Type Questions

7. Forming Polynomial from Sum and Product
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.
\[ \text{Sum of zeroes}=0,\qquad \text{Product of zeroes}=-9 \]
Variations: Sum and product of zeroes as \(5,-6\) and \(-10,24\).
Set 430/1/1
8. Verification of Relationship Between Zeroes and Coefficients
3 Marks
Find the zeroes of the polynomial \[ p(x)=3x^2-2x-1 \] and verify the relationship between the zeroes of \(p(x)\) and the coefficients of \(p(x)\).
Other variations: \[ 2x^2+5x+2, \quad 6x^2-5x-1, \quad 9s^2-6s+1, \] \[ 6x^2+13x-5, \quad 4x^2-4x-3, \quad 9x^2-6x-35, \quad 6x^2-7x-3. \]
Set 430/2/1
9. Forming a New Polynomial
3 Marks
If \(\alpha,\beta\) are zeroes of the polynomial \[ 3x^2-8x+4, \] then form a quadratic polynomial in \(x\) whose zeroes are \[ \frac{1}{\alpha} \quad\text{and}\quad \frac{1}{\beta}. \]
Set 430/5/1
10. Forming a New Polynomial – Scaled Zeroes
3 Marks
If \(\alpha,\beta\) are zeroes of the polynomial \[ 8x^2-5x-1, \] then form a quadratic polynomial in \(x\) whose zeroes are \[ \frac{2}{\alpha} \quad\text{and}\quad \frac{2}{\beta}. \]
Set 430/6/1
11. Finding the Unknown Coefficient \(k\)
3 Marks
\(\alpha,\beta\) are zeroes of the polynomial \[ 3x^2-8x+k. \] Find the value of \(k\), if \[ \alpha^2+\beta^2=\frac{40}{9}. \]
Set 430/5/3
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