Maths MCQ Ch-2 Class 10 | Polynomial

Mathematics

Multiple Choice Questions (MCQ)

Class 10 | Chapter 2 | Polynomials

MCQ Based on the different types of Polynomials

MCQ  Based on the Relationships between zeroes and coefficients.

MCQ Based on the Polynomials from the zeroes.

MCQ Based on the Quotient and Remainder obtained after dividing P(x) by g(x).

MCQ Based on the Division Algorithm.

MCQ Based from the CBSE Sample Questions

In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. Solution Hints are also given to some difficult problems. Each MCQ contains four options from which one option is correct. On the right hand side column of the pdf Answer option is given.

Action Plan

First of all students should Learn and write all basic points and Formulas related to the Polynomials.

Start solving  the NCERT Problems with examples.

Solve the important assignments on the Polynomials.

Then start solving the following MCQ.

MCQ | CHAPTER 2 | POLYNOMIALS

Q1) How many points will the graph of x² + 2x + 1 will cut the x-axis?
a) 3
b) 2
c) 1
d) 0
Ans: b

Q2) If the graph of a polynomial cuts the x-axis at 3 points, then the polynomial is a) Linear
b) Quadratic
c) Cubic
d) Biquadratic
Ans: c

Q3) What will be the nature of the zeros of a quadratic polynomial if it cuts the x-axis at two different points?
a) Real
b) Distinct
c) Real, Distinct
d) Complex 

Ans: c

Q4) Which of the following is a polynomial

a) x² + 2x + 5







Ans: a

Q5) Which of the following is not a polynomial ?
a) x² + 5x + 10
b) x ^{- 2} + 2x + 4
c) x¹² + 10x
d) 5x + 4 

Ans b

Q6) If the zeros of a polynomial are 3 and -5, then they cut the x-axis at ____ and _____ points.
a) (8, 0) and (-4, 0)
b) (3, -3) and (-5, 5)
c) (-3, 0) and (5, 0)
d) (3, 0) and (-5, 0)
Ans: d

Q7) The sum and product of zeros of a quadratic polynomial are 10 and 5/2 respectively. What will be the quadratic polynomial?
a) 2x² - 20x + 10
b) 2x² – x + 5
c) 2x² - 20x + 5
d) x² - 20x + 5 

Ans c

Q8) If α and β are the zeros of x² + 20x - 80, then the value of α + β is
a) -15
b) -5
c) -10
d) -20
Ans d


Q9) If α and β are the zeros of 3x² - 5x - 15, then the value of αβ is
a) -5
b) - 10
c) - 15
d) – 20
Ans: a


Q 10) What will be the value of other zero, if one zero of the quadratic polynomial is 5 and the sum of the zeros is 10?
a) 10
b) 5
c) -5
d) -10
Ans: b

Q 11) The value of a and b, if the zeros of x² + (a + 5)x - (b - 4) are -5 and 9 will be
a) 47, -5
b) -5, 47
c) -9, 49
d) -4, 45 

Ans: c

Q 12) If and are zeroes of  10x² + 20x – 80, then the value of     is

a) 5/ 4
b) 1/5
c) 3/ 4
d) 1/ 4 

Ans d

Q13) If α, β and γ are the zeros of 5x³ + 10x² – x + 20, then the value of αβγ is
a) -1
b) 5
c) -10
d) – 4
Ans: d


Q14) If α, β and γ are the zeros of 2x³ – 6x² + 5x + 2, then the value of α + β + γ is
a) 0
b) 1
c) 3
d) 2
Ans c


Q15) If the two zeros of the polynomial x³ – 9x² -x + 9, are 1 and 9, then the third zero is
a) 9
b) 1
c) 2
d) -1
Ans: d


Q 16) 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
Ans: d

Q 17) Find k, if one zero of polynomial kx² + 2x + (3k – 1) is 1

a) -1/ 2
b) 3/ 2
c) -1/ 4
d) - 3/ 2 

Ans: c

Q 18) A quadratic polynomial, whose zeroes are -4 and -5, is
(a) x² - 9x + 20
(b) x² + 9x + 20
(c) x² - 9x - 20
(d) x² + 9x - 20 

Ans b

Q19) If x³ + 1 is divided by x² + 5, then the possible degree of quotient is
(a) 0
(b) 1
(c) 2
(d) 3
Ans b

Q 20) If x³ + 11 is divided by x² – 3, then the possible degree of remainder is
(a) 0
(b) 1
(c) 2
(d) less than 2
Ans: d

Q21) Which of the following is not the graph of quadratic polynomial?

Ans: d

Q 22) If x⁵ + 2x⁴ + x + 6 is divided by g(x) and quotient is x² + 5x + 7, then the possible degree of remainder is:
(a) less than 1
(b) less than 2
(c) less than 3
(d) less than 4
Ans: c

Q 23) What is the number of zeroes that a linear polynomial has/have:
(a) 0
(b) 1
(c) 2
(d) 3 

Ans: b

Q 24) What is the number(s) of zeroes that a quadratic polynomial has/have:
(a) 0
(b) 1
(c) 2
(d) 3 

Ans c

Q 25) What is the number(s) of zeroes that a cubic polynomial has/have:
(a) 0
(b) 1
(c) 2
(d) 3 

Ans: d

Q 26) If one zero of the quadratic polynomial x² + 3x + b is 2, then the value of b is
(a) 10
(b) -8
(c) 9
(d) -10 

Ans: d

Q27) If 1 is one of the zeroes of the polynomial x² + x + k, then the value of k is:
(a) 2
(b) -2
(c) 4
(d) – 4
Ans : b

Q 28) If sum of zeroes of 2x² – kx + 3 is 2, then the value of k is
a) - 4
b) 2
c) – 2
d) 4 

Ans: d

Q 29) What is the degree of a zero polynomial
a) Less than 1
b) 0
c) Undefined
d) None of these
Ans: c

Q 30) If x⁴ + 3x² + 7 is divided by 3x + 5, then the possible degrees of quotient and remainder are:
(a) 3, 0
(b) 4, 1
(c) 3, 1
(d) 4, 0

Ans: a

Q 31) What is the degree of a linear polynomial :
a) 0
b) 1
c) 2
d) 3 

Ans: b

Q 32) Degree of a constant polynomial is :
a) 0
b) 1
c) 2
d) 3
Ans: a

Q 33) Graphical representation of a linear polynomial is :
a) Parabola
b) Origin
c) Straight Line
d) Circle
Ans: c

Q 34)Graphical representation of a quadratic polynomial is :
a) Parabola
b) Origin
c) Straight Line
d) Circle
Ans: a

Q 35) Form a quadratic polynomial whose zeroes are - 2 and 3 :
a) x² + x - 6
b) x² + x + 6
c) x² - x - 6
d) x² + 2x – 6
Ans: c

Q 36) The sum of zeroes of bx² + ax + c

 

 

 

 

Ans:  c

Q 37) If one zero of a quadratic polynomial ax² + bx + c is zero then c =
a) 0



Ans: a

Q 38) If sum of zeroes of 2x² – kx + 3 is 2, then k =
a) -4
b) 2
c) -2
d) 4
Ans : d
Q 39) If one zero of polynomial x² + px + 4 is 2, then find p
a) 4
b) -2
c) - 4
d) 2
Ans: c

Q 40) If one zero of 5x² – (k + 2)x + 3 is negative of the other then find k
a) 2
b) - 4
c) - 2
d) 4
Ans : c

Q 41)  Find a, if one zero of  ax² + (a - 4)x + 3 is reciprocal of other
a) - 3
b) 2
c) - 2
d) 3 

Ans: d

Q 42)   If     are zeroes of  2x² – 4x + 5  then   =  

a) 1
b) 4
c) - 1
d) - 4
Ans: c

Q 43)  Find k , If       are zeroes of  x² – 6x + k  such that  = 40

a) 2
b) - 3
c) 3
d) - 2
Ans: d

Q 44) A quadratic polynomial, whose zeroes are – 3 and 4, is

a) x² – x + 12                                              

b) x² - x - 12                     

c)  2x² – x + 18                                            

d) 2x² – x – 24

Ans:  b

Q 45)  Find k, if sum of zeroes of quadratic polynomial  3x² - (2k + 1)x – k + 5 is equal to the product of zeroes.
a)  4/3
b)  -4/3
c)  2/3
d)   -2/3

 Ans: a

Questions from CBSE Sample Paper 2021-22 
Basic Maths SP (241) & Standard Maths SP (041)

Q 46)  If -1 is a zero of the polynomial p(x) = x² - 7x - 8 , then the other zero is
(a) -8
(b) -7
(c) 1
(d) 8 

Ans: d

Q 47)  If 2 and 1 ⁄ 2 are the zeros of px² + 5x + r, then

(a) p = r = 2
(b) p = r = - 2
(c) p = 2, r = - 2
(d) p = - 2, r = 2 

Ans: b

Questions from CBSE final exam 2021-22 (241)

Q 48) The number of quadratic polynomials having zeroes - 2 and 5 is :
a) 1
b) 2
c) 3
d) More than 3 

Ans: a

Q 49)  If 1 is one of the zeroes of the polynomial P(x) = ax² – bx + 1, then
a) a + 1 = b
b) a – b = 0
c) a – b – 1 = 0
d) a + b = 1 

Ans: a

Q 50) The quadratic polynomial whose zeroes are  2 and  3 is :

a)  x² + 5x + 6                                        

b)  x² + 5x – 6

c)  x² - 5x + 6                                        

d)  x² - 5x – 6

Ans:  c

Q 51)  If (-2) is a zero of a polynomial  P(x) = x² + ax + 2b  and a + b = 4 then
a) a = 1, b = 3
b) a = 3, b = 1
c) a = -1, b = 5
d) a = 5, b = -1 

Ans: b

Q 52)  The graph of the polynomial y = p(x) is given in the figure. The number of zeroes of p(x) is :

a) 2
b) 4
c) 3
d) 1 

Ans: b

Q 53)  The parabola representing a quadratic polynomial p(x) = ax² + bx + c opens upward when :
a) a > 0
b) b > 0
c) c > 0
a < 0 

Ans: a

Questions from CBSE final exam 2021-22 (041)

Q 54)  If one of the zero of a quadratic polynomial  (k – 1)x² + kx + 1 is – 3, then the value of k is 
a)  4/3
b)  -4/3
c)  2/3
d)   -2/3

Ans: a

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