MCQ Questions For Class 10 Polynomials

Polynomials Class 10 MCQ is one of the best strategies to prepare for the CBSE Class 10 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more MCQ on Polynomials class 10, which will help them all through their board test.

Polynomials Class 10 MCQ Questions with Answer

Class 10 Math MCQ with answers are given here to chapter 2 Polynomials. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 10 Mathematics syllabus. By Solving these Class 10 MCQs, you will be able to analyze all of the concepts quickly in the chapter and get ready for the Class 10 Annual exam.

Learn Polynomials Class 10 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 10 Mathematics Polynomials MCQ with answers given below.

Question 1. If a, b are the zeroes of the polynomial f(x) = x² -3x +2, then 1/α 1/β + equals to: 
(a) 3
(b) –1
(c) 3/2
(d) – 3/2

Question 2. If the polynomial f(x) = ax³ + bx – c is divisible by the polynomial g(x) = x² + bx + c, then the value of ab 
is:
(a) 1/c
(b) 1
(c) –1
(d) none of these

Question 3. The quadratic polynomial having zeroes –3 and 2 is     
(a) x² – x -6
(b) x² + x -6
(c) x² + x +6
(d) x² – x +6

Question 4. The zeroes of the quadratic polynomial x² +99x +127 are   
(a) both positive
(b) both negative
(c) one positive and one negative
(d) both equal

Question 5. If a and 1/α  are the zeroes of polynomial 4x² -2x +(k- 4), the value of k is:   
(a) 4
(b) 8
(c) 0
(d) none of these

Question 6. The zeroes of 3x 2 +10x +7 3 are:   
(a) 7, 3
(b) √3,7 √3
(c) -√ 3 -7/√3,
(d) none of these

Question 7. If f(x) = ax² + bx + c has no real zeroes and a + b + c < 0, then:   
(a) c = 0
(b) c > 0
(c) c < 0
(d) none of these

Question 8. If a,b are the zeroes of the polynomial f(x) = ax² + bx + c, then 1/α² 1/β² + equals to:   
(a) b²-4ac/a² 
(b) b²-2ac/c² 
(c) b²-2ac/a² 
(d) b²+2ac/c²

Question 9. 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

Question 10. If p(x) = ax²+ bx + c has no real zero and a + b + c < 0, then   
(a) c = 0
(b) c < 0
(c) c > 0
(d) none of these

Question 11. If the sum of the zeroes of the polynomial f(x) = 2x³ -3kx² + 4x -5 is 6, then the value of k is:     
(a) 2
(b) 4
(c) –2
(d) –2

Question 12. If one root of the polynomial p(y) = 5y² +13y + m is reciprocal of other, then the value of m is   
(a) 6
(b) 0
(c) 5
(d) 1/5

Question 13. Given that one of the zeroes of the cubic polynomial ax³ + bx² + cx + d is zero, the product of the other two zeroes is   
(a) -c/a
(b) c/a
(c) 0
(d) -b/a

Question 14. A quadratic polynomial whose roots are –3 and 4 is 
(a) x² – x +12
(b) x² + x +12
(c) x²/2 – x/2-6
(d) 2x² +2x -24

Question 15. Which of the following is a polynomial: C
(a) x² + 1/x
(b) 2x² -3√x +1
(c) 3x² -3x +1
(d) x² + x ^-2 +7

Question 16. The product and sum of zeroes of the quadratic polynomial ax² + bx + c are respectively.
(a) b/a , c/a 
(b) c/a , b/a  
(c) c/b , 1
(d) c/a , -b/a

Question 17. If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it 
(a) has no linear term and the constant term is negative.
(b) has no linear term and the constant term is positive.
(c) can have a linear term but the constant term is negative.
(d) can have a linear term but the constant term is positive.

Question 18. If a and b are zeroes of p(x) = x² + x -1, then 1/α + 1/β + equals to   
(a) –1
(b) 1
(c) 2
(d) 0

Question 19. If one of the zeroes of the 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

Question 20. If the product of two zeroes of the polynomial p(x) = 2x³ +6x² – 4x +9 is 3, then its third zero is   
(a) -3/2
(b) 3/2
(c) -9/2
(d) 9/2

Question 21. If √(5/3) and -√(5/3) are two zeroes of the polynomial 3x⁴ +6x³ -2x² -10x -5, then its other two zeroes are:   
(a) –1, –1
(b) 1, –1
(c) 1, 1
(d) 3, –3

Question 22. If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it 
(a) has no linear term and the constant term is negative.
(b) has no linear term and the constant term is positive.
(c) can have a linear term but the constant term is negative.
(d) can have a linear term but the constant term is positive.

Question 23. If the zeroes of the quadratic polynomial ax²+ 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

Question 24. If the graph of a polynomial intersects the x-axis at exactly two points, then it   
(a) cannot be a linear or a cubic polynomial
(b) can be a quadratic polynomial only
(c) can be a cubic or a quadratic polynomial
(d) can be a linear or a quadratic polynomial

Question 25. A quadratic polynomial with 3 and 2 as the sum and product of its zeroes respectively is 
(a) x² +3x -2
(b) x² -3x +2
(c) x² -2x +3
(d) x² -2x -3

Whoever needs to take the CBSE Class 10 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 10 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Polynomials class 10 MCQ are ready by the subject specialists themselves.

Question 26. Given that two of the zeroes of the cubic polynomial ax³ + bx 2 + cx + d are 0, the value of c is   
(a) less than 0
(b) greater than 0
(c) equal to 0
(d) can’t say

Question 27. If a and b are zeroes of p(x) = x² + x -1, then 1/α + 1/β + equals to   
(a) –1
(b) 1
(c) 2
(d) 0

Question 28. If 5 is a zero of the quadratic polynomial x² – kx -15, then the value of k is 
(a) 2
(b) –2
(c) 4
(d) – 4

Question 29. Given that two of the zeroes of the cubic polynomial ax³ + bx² + cx + d are 0, the value of c is   
(a) less than 0
(b) greater than 0
(c) equal to 0
(d) can’t say

Question 30. If the zeroes of the quadratic polynomial ax² + bx + c, c ¹ 0 are equal, then   
(a) c and a have opposite signs
(b) c and a have the same sign
(c) c and b have opposite signs
(d) c and b have the same sign

Question 31. If the zeroes of the quadratic polynomial ax² + bx + c, c ¹ 0 are equal, then   
(a) c and a have opposite signs
(b) c and a have the same sign
(c) c and b have opposite signs
(d) c and b have the same sign

Question 32. Given that one of the zeroes of the cubic polynomial ax³ + bx² + cx + d is zero, the product of the other two zeroes is   
(a) -c/a  
(b) c/a  
(c) 0
(d) -b/a

Question 33. If one of the zeroes of a quadratic polynomial of the form x²  + ax + b is negative of the other, then it 
(a) has no linear term and the constant term is negative
(b) has no linear term and the constant term is positive
(c) can have a linear term but the constant term is positive
(d) can have a linear term but the constant term is negative

Question 34. If one zero of the quadratic polynomial x²  -5x + k is –4 ,then the value of k is   
(a) 36
(b) –36
(c) 18
(d) –18

Question 35. The zeroes of the quadratic polynomial x² + kx + k, k ≠ 0   
(a) cannot both be positive
(b) cannot both be negative
(c) are always equal
(d) are always unequal

Question 36. If a polynomial of degree 6 is divided by a polynomial of degree 2, then the degree of the quotient is 
(a) less than 4
(b) less than 2
(c) equal to 2
(d) equal to 4

Question 37. 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

Question 38. The zeroes of the quadratic polynomial x² + ax + b a, b > 0 are   
(a) both positive
(b) both negative
(c) one positive one negative
(d) can’t say

Question 39. A quadratic polynomial with sum and product of its zeroes as 8 and –9 respectively is   
(a) x²  -8x +9
(b) x²  -8x -9
(c) x²  +8x -9
(d) x²  +8x +9

Question 40. If one of the zeroes of the cubic polynomial x 3 + ax² + bx + c is –1, then the product of the other two zeroes is   
(a) a – b -1
(b) b – a -1
(c) b – a +1
(d) a – b +1

Question 41. The degree of the remainder r(x) when p(x)= bx³ + cx + d is divided by a polynomial of degree 4 is   
(a) less than 4
(b) less than 3
(c) equal to 3
(d) less than or equal to 3

Question 42. A quadratic polynomial, whose zeroes are 5 and –8 is   
(a) x² +13x – 40
(b) x² + 4x -3
(c) x² -3x + 40
(d) x² +3x – 40

Question 43. The number of polynomials having exactly two zeroes 1 and –2 is   
(a) 1
(b) 2
(c) 3
(d) infinitely many

Question 44. If the zeroes of the algebraic expression 3ax² + x(3b + 5a are -3/7 and -5/3 , then find the value of a/b
(a) 1/3
(b) 4/5
(c) 7/3
(d) 3
(e) None of these

Question 45. Solve

Question 46. If α,β,y are the zeroes of the polynomial p(x) = x³ – ax² + bx – c then 1/αβ + 1/αβ + 1/αβ = __________
(a) a/b
(b) b/c
(c) a/c
(d) c/d
(e) None of these

Question 47. If two zeroes of the polynomial f (x) = x⁴ – 2x³ – 18x² – 6x + 45 are , -√3 and √3 then find the sum of other two zeroes.
(a) 0
(b) -1
(c) -2
(d) 1
(e) None of these

Question 48. if p(x) = x² + x + 1 and q (x) = x³ – x + 1, then the HCF of p (b) and q (a)
(a) c + b + 1
(b) a – b + 1
(c) a – b
(d) a + b
(e) None of these

Question 49. If p and q are the zeroes of the quadratic polynomial f(x) = ax² + ax + b then the value of p⁴ + q⁴ is ______
(a) (a² – 2bc)² – b²c²/c⁴
(b) (a² – 2bc)² – 2b²c²/c⁴
(c) (b² – 2ac)² – a²c²/c⁴
(d) (b² – 2ac)² – 2a²c²/c⁴
(e) None of these

Question 50. If the zeroes of the polynomial f(x) = ax³ + 3bx² 3cx + d are in A.P. then 2b³ + a²d is equal to _______
(a) a² bc
(b) 3abc
(c) 2b² ac
(d) abc
(e) None of these

Question 51. If the LCM of p(x) and q(x) is a⁹ b⁹ then their HCF can be
(a) (a – b)
(b) (a² + b² + ab)
(c) a⁶ + b⁶ + a³b³
(d) all the above
(e) none of these

Question 52. The graph of a polynomial f(x) is shown below:

The number of real zeroes of the polynomial f(x) is _________
(a) 1
(b) 2
(c) 3
(d) 4
(e) None of these

Question 53. If f(x) = 3x⁴ + 6x³ – 2x^{2 –} l0x – 5 and two of its zeroes are – 1, – 1, then the other two zeroes are _______
(a) √3/5 – √3/5
(b) √2/5 – √2/5
(c) √5/3 – √5/3
(d) √5/4 – √5/4
(e) None of these

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