CHAPTER 2 : POLYNOMIALS
CBSE Class 10 Mathematics — Standard | PYQs 2025
SECTION A : MULTIPLE CHOICE QUESTIONS (1 Mark Each)
1.
If α and β are the zeroes of polynomial
3x² + 6x + k such that
α + β + αβ = −2/3, then the value of k is:
(A) −8
(B) 8
(C) −4
(D) 4
[Series 30/1/1]
2.
Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is:
(A) 3
(B) 5
(C) 2
(D) 4
[Series 30/1/1, Q10; Series 30/1/3, Q6]
3.
The sum of the zeroes of the polynomial
p(x) = 5x − 7x² + 3 is:
(A) −7/5
(B) 7/5
(C) 5/7
(D) −5/7
[Series 30/1/3, Q11]
4.
If −4 is a zero of the polynomial
p(x) = x² − x − (2 + 2k),
then the value of k is:
(A) 3
(B) 9
(C) 6
(D) −9
[Series 30/2/1, Q16; Series 30/2/2, Q5]
5.
If one zero of the polynomial
q(x) = (p² + 4)x² + 65x + 4p
is reciprocal of the other, then the value of p is:
(A) −1
(B) 1
(C) −2
(D) 2
[Series 30/2/3, Q5]
6.
If α and β are the zeroes of the polynomial
p(x) = x² − ax − b,
then the value of
(α + β + αβ) is equal to:
(A) a + b
(B) −a − b
(C) a − b
(D) −a + b
[Series 30/3/1, Q4]
7.
Zeroes of the polynomial
p(x) = x² − 3√2x + 4 are:
(A) 2, √2
(B) 2√2, √2
(C) 4√2, −√2
(D) √2, 2
[Series 30/3/1, Q17; Series 30/3/3, Q12]
8.
Zeroes of the polynomial
p(y) = 7y² − (11/3)y − 2/3 are:
(A) −2/3, −1/7
(B) −2/7, −1/3
(C) 2/3, 1/7
(D) 2/3, −1/7
[Series 30/3/2, Q6]
9.
If α and β are zeroes of the polynomial
p(x) = kx² − 30x + 45k
and
α + β = αβ,
then the value of k is:
(A) −2/3
(B) −3/2
(C) 3/2
(D) 2/3
[Series 30/3/3, Q4]
10.
Which of the following statements is true for a polynomial
p(x) of degree 3?
(A) p(x) has at most two distinct zeroes.
(B) p(x) has at least two distinct zeroes.
(C) p(x) has exactly three distinct zeroes.
(D) p(x) has at most three distinct zeroes.
[Series 30/4/1, Q17; Series 30/4/2, Q1; Series 30/4/3, Q8]
11.
If the zeroes of the polynomial
ax² + bx + 2a/b
are reciprocal of each other, then the value of b is:
(A) 2
(B) 1/2
(C) −2
(D) −1/2
[Series 30/6/1, Q4; Series 30/6/2, Q6; Series 30/6/3, Q13]
SECTION B : VERY SHORT ANSWER QUESTIONS (2 Marks Each)
12.
Find the zeroes of the polynomial
p(x) = x² + x/6 − 1/6.
[Series 30/1/1, Q22]
13.
Find the zeroes of the polynomial
p(x) = x² + (4/3)x − 4/3.
[Series 30/1/3, Q24]
14.
If p and q are zeroes of the polynomial
p(y) = 21y² − y − 2,
then find the value of
(1 − p)(1 − q).
[Series 30/2/1, Q21; Series 30/2/3, Q23]
15.
Find a quadratic polynomial whose zeroes are
2 and
−7/5.
[Series 30/2/2, Q21]
16.
If α and β are the zeroes of the polynomial
p(y) = y² − 5y + 3,
then find the value of
α⁴β³ + α³β⁴.
[Series 30/3/1, Q24(b); Series 30/3/3, Q22(b)]
17.
If the sum of the zeroes of the polynomial
p(x) = (p + 1)x² + (2p + 3)x + (3p + 4)
is −1, then find the value of p.
[Series 30/3/2, Q21(a)]
18.
If α and β are zeroes of the polynomial
p(x) = x² − 2x − 1,
then find the value of
1/(2α) + 1/(2β) + 3αβ.
[Series 30/3/2, Q21(b)]
SECTION C : SHORT ANSWER QUESTIONS (3 Marks Each)
19.
α and β are zeroes of a quadratic polynomial
px² + qx + 1.
Form a quadratic polynomial whose zeroes are
2/α and
2/β.
[Series 30/4/1, Q30]
20.
α and β are zeroes of a quadratic polynomial
x² − ax − b.
Obtain a quadratic polynomial whose zeroes are
3α + 1 and
3β + 1.
[Series 30/4/2, Q26]
21.
If α and β are the zeroes of the polynomial
ax² − x + c,
obtain a polynomial whose zeroes are
α − 3 and
β − 3.
[Series 30/4/3, Q28]
22.
Obtain the zeroes of the polynomial
7x² + 18x − 9.
Hence, write a polynomial each of whose zeroes is twice the zeroes of the given polynomial.
[Series 30/5/1, Q27]
23.
Obtain the zeroes of the polynomial
p(x) = 2x² − 5x − 3.
Hence, obtain a polynomial each of whose zeroes is one less than each of the zeroes of p(x).
[Series 30/5/2, Q29]
24.
Find the zeroes of the polynomial
p(x) = 6x² − 5x − 1.
Hence, obtain a polynomial each of whose zeroes is three times the zeroes of p(x).
[Series 30/5/3, Q26]
25.
Find the zeroes of the polynomial
p(x) = 3x² − 4x − 4.
Hence, write a polynomial whose each of the zeroes is 2 more than the zeroes of p(x).
[Series 30/6/1, Q27]
26.
Find the zeroes of the polynomial
q(x) = 8x² − 2x − 3.
Hence, find a polynomial whose zeroes are 2 less than the zeroes of q(x).
[Series 30/6/2, Q29]
27.
Find the zeroes of the polynomial
r(x) = 4x² + 3x − 1.
Hence, write a polynomial whose zeroes are reciprocal of the zeroes of polynomial r(x).
[Series 30/6/3, Q31]