MCQ Questions for Class 10 Maths Polynomials with Answers

MCQ Questions for Class 10 Maths Polynomials with Answers

Free PDF Download of CBSE Class 10 Maths Chapter 2 Polynomials Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Polynomials MCQs with Answers to know their preparation level.

MCQ Questions for Class 10 Maths Polynomials with Answers

1. If one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is
(a) 10
(b) -10
(c) 5
(d) -5

Answer

Answer: b


2. Given that two of the zeroes of the cubic poly-nomial ax3 + bx² + cx + d are 0, the third zero is
MCQ Questions for Class 10 Maths Polynomials with Solutions 1

Answer

Answer: a


3. If one of the zeroes of the quadratic polynomial (k - 1) x² + kx + 1 is - 3, then the value of k is
MCQ Questions for Class 10 Maths Polynomials with Solutions 2

Answer

Answer: a


4. A quadratic polynomial, whose zeroes are -3 and 4, is
(a) x²- x + 12
(b) x² + x + 12
(c) \frac{x^{2}}{2}-\frac{x}{2}-6
(d) 2x² + 2x - 24

Answer

Answer: c


5. 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

Answer

Answer: d


6. The number of polynomials having zeroes as -2 and 5 is
(a) 1
(b) 2
(c) 3
(d) more than 3

Answer

Answer: d


7. Given that one of the zeroes of the cubic polynomial ax3 + bx² + cx + d is zero, the product of the other two zeroes is
MCQ Questions for Class 10 Maths Polynomials with Solutions 3

Answer

Answer: b


8. If one of the zeroes of the cubic polynomial x3 + ax² + bx + c is -1, then the product of the
other two zeroes is
(a) b - a + 1
(b) b - a - 1
(c) a - b + 1
(d) a - b - 1

Answer

Answer: a


9. 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

Answer

Answer: b


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

Answer

Answer: a


11. 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

Answer

Answer: c


12. 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.

Answer

Answer: a


14. The number of polynomials having zeroes as 4 and 7 is
(a) 2
(b) 3
(c) 4
(d) more than 4

Answer

Answer: d


15. A quadratic polynomial, whose zeores are -4 and -5, is
(a) x²-9x + 20
(b) x² + 9x + 20
(c) x²-9x- 20
(d) x² + 9x- 20

Answer

Answer: b


16. The zeroes of the quadratic polynomial x² + 1750x + 175000 are
(a) both negative
(b) one positive and one negative
(c) both positive
(d) both equal

Answer

Answer: a


17. The zeroes of the quadratic polynomial x² - 15x + 50 are
(a) both negative
(b) one positive and one negative
(c) both positive
(d) both equal

Answer

Answer: c


18. The zeroes of the quadratic polynomial 3x² - 48 are
(a) both negative
(b) one positive and one negative
(c) both positive
(d) both equal

Answer

Answer: b


19. The zeroes of the quadratic polynomial x² - 18x + 81 are
(a) both negative
(b) one positive and one negative
(c) both positive and unequal
(d) both equal and positive

Answer

Answer: d


20. The zeroes of the quadratic polynomial x² + px + p, p ≠ 0 are
(a) both equal
(b) both cannot be positive
(c) both unequal
(d) both cannot be negative

Answer

Answer: b


22. If the zeroes of the quadratic polynomial Ax² + Bx + C, C # 0 are equal, then
(a) A and B have the same sign
(b) A and C have the same sign
(c) B and C have the same sign
(d) A and C have opposite signs

Answer

Answer: b


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

Answer

Answer: b


24. 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

Answer

Answer: d


25. 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

Answer

Answer: a


26. If x5 + 2x4 + x + 6 is divided by g(x), and quotient is x² + 5x + 7, then the possible degree of g(x) is:
(a) 4
(b) 2
(c) 3
(d) 5

Answer

Answer: c


27. If x5 + 2x4 + x + 6 is divided by g(x) and quo-tient 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

Answer

Answer: c


28. What is the number of zeroes that a linear poly-nomial has/have:
(a) 0
(b) 1
(c) 2
(d) 3

Answer

Answer: b


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

Answer

Answer: c


30. What is the number(s) of zeores that a cubic polynomial has/have:
(a) 0
(b) 1
(c) 2
(d) 3

Answer

Answer: d


31. If one of the zeroes of the cubic polynomial x3 + px² + qx + r is -1, then the product of the other two zeroes is
(a) p + q + 1
(b) p-q- 1
(c) q - p + 1
(d) q - p - 1

Answer

Answer: c


32. 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

Answer

Answer: d


33. 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

Answer

Answer: b


34. If p(x) is a polynomial of at least degree one and p(k) = 0, then k is known as
(a) value of p(x)
(b) zero of p(x)
(c) constant term of p{x)
(d) none of these

Answer/Explanation

Answer: b
Explaination:
Zero of p(x)
Let p(x) = ax + b
Put x = k
p(k) = ak + b = 0
∴ k is zero of p(x).


36. If the zeroes of the quadratic polynomial x² + (a + 1) x + b are 2 and -3, then [NCERT Exemplar Problem, CBSE 2011]
(a) a = -7, b = -1
(b) a = 5, b = -1
(c) a = 2, b = -6
(d) a = 0, b = -6

Answer/Explanation

Answer: d
Explaination:
x² + (a + 1)x + b
∵ x = 2 is a zero
and x = - 3 is another zero
∴ (2)² + (a + 1)² + 6 = 0
and (- 3)² + (a + 1) (- 3) + b = 0
⇒ 4 + 2cr + 2 + & = 0
and 9 - 3a - 3 + b = 0
⇒ 2a + b = - 6 …(i)
and - 3a + b = - 6 …(ii)
Solving (i) and (ii), we get 5a = 0
⇒ a = 0 and b = - 6.


38. Zeroes of a polynomial can be determined graphically. No. of zeroes of a polynomial is equal to no. of points where the graph of polynomial
(a) intersects y-axis
(b) intersects x-axis
(c) intersects y-axis or intersects x-axis
(d) none of these

Answer/Explanation

Answer: b
Explaination:
(b) Intersects x-axis.


39. If graph of a polynomial does not intersects the x-axis but intersects y-axis in one point, then no. of zeroes of the polynomial is equal to
(a) 0
(b) 1
(c) 0 or 1
(d) none of these

Answer/Explanation

Answer: a
Explaination:
(a) Zero


40. A polynomial of degree n has
(a) only 1 zero
(b) at least n zeroes
(c) atmost n zeroes
(d) more than n zeroes

Answer/Explanation

Answer: c
Explaination:
Maximum number of zeroes of a
polynomial = degree of the polynomial.


41. If p(x) = axr + bx + c, then –\frac{b}{a} is equal to
(a) 0
(b) 1
(c) product of zeroes
(d) sum of zeroes

Answer/Explanation

Answer: d
Explaination:
(d) Sum of zeroes = –\frac{b}{a}


42. If p(x) = ax² + bx + c one zero is and a + b + c = 0, then one zero is
(a) \frac{-b}{a}
(b) \frac{c}{a}
(c) \frac{b}{c}
(d) none of these

Answer/Explanation

Answer: b
Explaination:
p(1) = 0; a(1)² + b(1) + c = 0
⇒ a + b + c = 0
∴ one zero (α) = 1
αβ = product of zeroes = \frac{c}{a}
⇒ 1.β = \frac{c}{a}
⇒ β = \frac{c}{a}
∴ zeroes are 1 and \frac{c}{a}


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