MCQ Questions | Class 10 Maths Chapter 2 | Polynomials with Answers

MCQ | Polynomials Class 10 | Sat C

Check the below NCERT MCQ Questions for Class 10 Maths Chapter 2 Polynomials with Answers Pdf free download. MCQ Questions for Class 10 Maths with Answers were prepared based on the latest exam pattern. We have Provided Polynomials Class 10 Maths MCQs Questions with Answers to help students understand the concept very well.

Objective Question | NCERT Maths Class 10

NCERT Solutions Class 10 Maths
Book:	National Council of Educational Research and Training (NCERT)
Board:	Central Board of Secondary Education (CBSE)
Class:	10th
Subject:	Maths
Chapter:	2
Chapters Name:	Polynomials
Medium:	English

Ncert Solutions for Class 10 Maths | Objective Type Questions

You can refer to NCERT Solutions for Class 10 Maths Chapter 2 Polynomials to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

Polynomials | Class 10 Maths | NCERT Solutions

Q1.	What is the number(s) of zeores that a cubic polynomial has/have:
	A. 0
	B. 1
	C. 2
	D. 3

Ans: 3

Q2.	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

Ans: q – p + 1

Q3.	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: -1

Q4.	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: -2

Q5.	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

Ans: zero of p(x)

Q6.	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: a = , b = -6

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.

Q7.	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

Ans: A and C have the same sign

Q8.	If x = 2 and x = 3 are zeros of the quadratic polynomial x² + ax + b, the values of a and b respectively are :
	A. 5, 6
	B. - 5, - 6
	C. - 5, 6
	D. 5, - 6

Ans: - 5, 6

Q9.	The graph of the polynomial f(x) = 2x – 5 intersects the x – axis at
	A. (5/2, 0)
	B. (-5/2, 0)
	C. (-5/2, 5/2)
	D. (5/2, -5/2)

Ans: (5/2, 0)

Q10.	Sum and the product of zeroes of the polynomial x² +7x +10 is
	A. 10/7 and -10/7
	B. 7/10 and -7/10
	C. -7 and 10
	D. 7 and -10

Ans: -7 and 10

Q11.	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

Ans: intersects x-axis

Q12.	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

Ans:

Q13.	A polynomial of degree n has
	A. only 1 zero
	B. at least n zeroes
	C. atmost n zeroes
	D. more than n zeroes

Ans: atmost n zeroes

Explaination:

Maximum number of zeroes of a
polynomial = degree of the polynomial.

Q14.	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

Ans: sum of zeroes

Q15.	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

Ans: \(\frac{c}{a}\)

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 \(\frac{c}{a}\)

Q16.	The number of polynomials having zeroes as -2 and 5 is
	A. 1
	B. 2
	C. 3
	D. more than 3

Ans: more than 3

Explaination:

∵ x² – 3x – 10, 2x² – 6x – 20,
\(\frac{1}{2}\)x² – \(\frac{3}{2}\)x – 5, 3x² – 9x – 30 etc.,
have zeroes – 2 and 5.

Q17.	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.

Ans: has no linear term and the constant term is negative.

Explaination:

f(x) = x² + ax + b
Given: zeroes are α and – α
Sum of zeroes = α – α = 0
∴ f(x) = x² + b, which is not linear
Product of zeroes = α(-α) = – α² = \(\frac{b}{1}\)
⇒ -α² = b
It is possible when, b < 0.
Hence, it has no linear term and the constant term is negative.

Q18.	If 4x² – 6x – m is divisible by x – 3, the value of m is exact divisor of
	A. 9
	B. 45
	C. 20
	D. 36

Ans: 9

Explaination:

Here p(3) = 0
⇒ 4(3)² – 6 × 3-m = 0
⇒ 36 – 18 – m = 0
⇒ m=18
∴ Value of m is exactly divisible by 9.

Q19.	Which one of the following statements is correct
	A. if x⁶ + 1 is divided by x + 1, then the remainder is -2.
	B. if x⁶ + 1 is divided by x – 1, then the remainder is 2.
	C. if x⁶ + 1 is divided by x + 1, then the remainder is 1.
	D. if x⁶ + 1 is divided by x – 1, then the remainder is -1.

Ans: if x⁶ + 1 is divided by x – 1, then the remainder is 2.

Explaination:

p(x) = x⁶ + 1
when divided by x – 1, then remainder = p(1)
∴ p(1) = 1⁶ + 1 = 2

Q20.	Consider the following statements (i) x – 2 is a factor of x³ – 3x² + 4x – 4. (ii) x + 1 is a factor of 2x³ + 4x + 6. (iii) x – 1 is a factor of x⁵ + x⁴ – x³ + x² -x + 1. In these statements
	A. 1 and 2 are correct
	B. 1, 2 and 3 are correct
	C. 2 and 3 are correct
	D. 1 and 3 are correct

Ans: 1 and 2 are correct

Explaination:

x – 2 is a factor of x³ – 3x² + 4x – 4
∵ remainder is zero Similarly x + 1 is a factor of 2x³ + 4x + 6
but x – 1 is not a factor of x⁵ + x⁴ – x³ + x² – x + 1
∵ remainder is not zero
∴ Statements 1 and 2 are correct.

CBSE Solutions | Ncert Solutions Maths Class 10

NCERT Solutions | 10th Maths Guide

NCERT | Class 10 Maths Solution

Ncert Solutions for Class 10 Maths

MCQ Questions | Class 10 Maths Chapter 2

MCQ Questions | Class 10 Maths Chapter 2 | Polynomials with Answers

MCQ | Polynomials Class 10 | Sat C

Objective Question | NCERT Maths Class 10

Ncert Solutions for Class 10 Maths | Objective Type Questions

Polynomials | Class 10 Maths | NCERT Solutions

CBSE Solutions | Ncert Solutions Maths Class 10

NCERT Solutions | 10th Maths Guide

NCERT | Class 10 Maths Solution

Ncert Solutions for Class 10 Maths

Ncert Solutions for Class 10 Maths Chapter 1

Ncert Solutions for Class 10 Maths Chapter 2

Ncert Solutions for Class 10 Maths Chapter 3

Ncert Solutions for Class 10 Maths Chapter 4

Ncert Solutions for Class 10 Maths Chapter 5

Ncert Solutions for Class 10 Maths Chapter 6

Ncert Solutions for Class 10 Maths Chapter 7

Ncert Solutions for Class 10 Maths Chapter 8

Ncert Solutions for Class 10 Maths Chapter 9

Ncert Solutions for Class 10 Maths Chapter 10

Ncert Solutions for Class 10 Maths Chapter 11

Ncert Solutions for Class 10 Maths Chapter 12

Ncert Solutions for Class 10 Maths Chapter 13

Ncert Solutions for Class 10 Maths Chapter 14

Ncert Solutions for Class 10 Maths Chapter 15

NCERT SOLUTIONS

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