Next topper module

Part - 1 (Basic Multiple Choice Questions)
1. The maximum number of zeroes that a polynomial of degree 3 can have is [CBSE 2012]
(a) One (b) Two (c) Three (d) None
2. The given linear polynomial y = f(x) has [CBSE SQP (Standard) 2023-24]
Y

5



4 (0, 4)



3



2



1


(3, 0)
X’ X
–1 O 1 2 3 4

Y’


(a) 2 zeroes (b) 1 zero and the zero is ‘3’
(c) 1 zero and the zero is ‘4’ (d) No zero
3. The graph of a polynomial is shown in figure, then the number of its zeroes is [CBSE (Basic) 2020]

Y




O
x’ X




Y’

(a) 3 (b) 1 (c) 2 (d) 4
4. If –2 is a zero of the polynomial P(x) = 3x + 4x + 2k, then the value of k is
2


(a) 1 (b) –1 (c) 2 (d) –2


Polynomials 1

,5. The zeroes of the quadratic polynomial x2 + 99x + 127 are [CBSE 2010]
(a) Both positive (b) Both negative
(c) One positive and one negative (d) Both equal

6. The zeroes of the quadratic polynomial x 2  kx  k, k  0
(a) Cannot both be positve (b) Cannot both be negative
(c) Are always unequal (d) Are always equal.

7. If the zeroes of the quadratic polynomial ax 2  bx  c, c  0 are equal, then
(a) c and a have opposite, signs (b) c and b have opposite signs
(c) c and a have the same sign (d) c and b have the same sign

8. If the sum of zeroes of the polynomial x 2   k  3 x   5k  3 is equal to one-fourth of the product of the zeroes,
then the value of k is
(a) 3 (b) 5 (c) 15 (d) 18
9. The quadratic polynomial, the sum of whose zeroes is –5 and their product is 6, is [CBSE (Standard) 2020]

(a) x 2  5x  6 (b) x 2  5x  6 (c) x 2  5x  6 (d)  x 2  5x  6

5 5
10. A quadratic polynomial having zeroes  and is [CBSE SQP (Standard) 2024-25]
2 2

(d) x  2 5 x  1
2
(a) x 2  5 2x  1 (b) 8x 2  20 (c) 15x 2  6

11. If a and b are zeroes of the polynomial 2t 2  4t  3 , then the value of a 2 b  ab 2 is :

3
(a) (b) 2 (c) 3 (d) 4
4
12. While observing a basketball player in action, Pratham wondered if the path traced by the ball during its journey
from the player's hands to the basket is that of a parabola. On reaching home, he traced the path on a graph paper
and was happy to learn that it indeed resembles the shape of a parabola, which is the graph of a quadratic polynomial.
He thought that he can also evaluate the zeroes of this polynomial.




If the zeroes of the quadratic polynomial x² + (a + 1) x + b are 2 and –3, then:
(a) a = –7, b = –1 (b) a = 5, b = –1 (c) a = 2, b = – 6 (d) a = 0, b = – 6



Class - X (Module • Mathematics) 2

, 1
13. If ,  are the zeroes of the quadratic polynomial p(x) = x² – (k + 6) x + 2(2k – 1), then the value of k, if     
2
is : [CBSE Term-1 Std. 2021]
(a) –7 (b) 7 (c) –3 (d) 3

14. If ,  are zeroes of the polynomial x² – 1, then value of      is : [CBSE 2023]
(a) 2 (b) 1 (c) –1 (d) 0


Part - 2 (Basic Subjective Type Questions)
1. Find out the degrees of following polynomials.

(a) p  x   7x  5x 2  3 (b) q  x   5x 4  32x 2  5x  8

1
(c) r  x   x 3  x 6  5 2 (d) h  x    3x
2

2. Find the zeroes of the quadratic polynomial 6x 2  3  7x and verify the relationship between the zeroes and the
coefficients.

2
3. If zeroes of the polynomial x 2  4x  2a are  and , then find the value of a.


4. If ,  are zeroes of quadratic polynomial 5x 2  5x  1, find the value of

(i)  2  2 (ii)  1  1

5. If  and  are zeroes of a polynomial 6x 2  5x  1 then form a quadratic polynomial whose zeroes are
 2 and  .
2
[CBSE SQP 2024]
6. If m and n are zeroes of the polynomial without factorising the polynomial. [CBSE Question Bank 2023]
(3x – x – 2), find the values of the following.
2



1 1
(a)  (b) m2  n 2
m n




Polynomials 3