Maths MCQ Ch-2 Class 10 | Polynomial

Mathematics

Multiple Choice Questions (MCQ)

Class 10 | Chapter 2 | Polynomials

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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