# NCERT solutions for Mathematics Exemplar Class 10 chapter 2 - Polynomials [Latest edition]

## Chapter 2: Polynomials

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4
Exercise 2.1 [Pages 9 - 10]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 2 Polynomials Exercise 2.1 [Pages 9 - 10]

Exercise 2.1 | Q 1 | Page 9

If one of the zeroes of the quadratic polynomial (k – 1)x2 + k x + 1 is – 3, then the value of k is ______.

• 4/3

• (-4)/3

• 2/3

• (-2)/3

Exercise 2.1 | Q 2 | Page 9

A quadratic polynomial, whose zeroes are –3 and 4, is ______.

• x^2 - x + 12

• x^2 + x + 12

• x^2/2 - x/2 - 6

• 2x^2 + 2x - 24

Exercise 2.1 | Q 3 | Page 9

If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and –3, then ______.

• a = –7, b = –1

• a = 5, b = –1

• a = 2, b = – 6

• a = 0, b = – 6

Exercise 2.1 | Q 4 | Page 9

The number of polynomials having zeroes as –2 and 5 is ______.

• 1

• 2

• 3

• More than 3

Exercise 2.1 | Q 5 | Page 9

Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is ______.

• - c/a

• c/a

• 0

• - b/a

Exercise 2.1 | Q 6 | Page 9

If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is –1, then the product of the other two zeroes is ______.

• b – a + 1

• b – a – 1

• a – b + 1

• a – b –1

Exercise 2.1 | Q 7 | Page 10

The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.

• Both positive

• Both negative

• One positive and one negative

• Both equal

Exercise 2.1 | Q 8 | Page 10

The zeroes of the quadratic polynomial x2 + kx + k, k ≠ 0 ______.

• Cannot both be positive

• Cannot both be negative

• Are always unequal

• Are always equal

Exercise 2.1 | Q 9 | Page 10

If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then ______.

• c and a have opposite signs

• c and b have opposite signs

• c and a have the same sign

• c and b have the same sign

Exercise 2.1 | Q 10 | Page 10

If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it ______.

• Has no linear term and the constant term is negative

• Has no linear term and the constant term is positive

• Can have a linear term but the constant term is negative

• Can have a linear term but the constant term is positive

Exercise 2.1 | Q 11 | Page 10

Which of the following is not the graph of a quadratic polynomial?

Exercise 2.2 [Pages 11 - 12]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 2 Polynomials Exercise 2.2 [Pages 11 - 12]

#### Answer the following and justify:

Exercise 2.2 | Q 1.(i) | Page 11

Can x2 – 1 be the quotient on division of x6 + 2x3 + x – 1 by a polynomial in x of degree 5?

Exercise 2.2 | Q 1.(ii) | Page 11

What will the quotient and remainder be on division of ax2 + bx + c by px3 + qx2 + rx + s, p ≠ 0?

Exercise 2.2 | Q 1.(iii) | Page 11

If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, what is the relation between the degrees of p(x) and g(x)?

Exercise 2.2 | Q 1.(iv) | Page 11

If on division of a non-zero polynomial p(x) by a polynomial g(x), the remainder is zero, what is the relation between the degrees of p(x) and g(x)?

Exercise 2.2 | Q 1.(v) | Page 11

Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?

Exercise 2.2 | Q 2.(i) | Page 11

If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.

• True

• False

Exercise 2.2 | Q 2.(ii) | Page 11

If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial.

• True

• False

Exercise 2.2 | Q 2.(iii) | Page 11

If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial.

• True

• False

Exercise 2.2 | Q 2.(iv) | Page 11

If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

• True

• False

Exercise 2.2 | Q 2.(v) | Page 12

If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.

• True

• False

Exercise 2.2 | Q 2.(vi) | Page 12

If all three zeroes of a cubic polynomial x3 + ax2 – bx + c are positive, then at least one of a, b and c is non-negative.

• True

• False

Exercise 2.2 | Q 2.(vii) | Page 12

The only value of k for which the quadratic polynomial kx2 + x + k has equal zeros is 1/2

• True

• False

Exercise 2.3 [Pages 12 - 13]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 2 Polynomials Exercise 2.3 [Pages 12 - 13]

Exercise 2.3 | Q 1.(i) | Page 12

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

4x2 – 3x – 1

Exercise 2.3 | Q 1.(ii) | Page 12

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

3x2 + 4x – 4

Exercise 2.3 | Q 1.(iii) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

5t2 + 12t + 7

Exercise 2.3 | Q 1.(iv) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

t3 – 2t2 – 15t

Exercise 2.3 | Q 1.(v) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

2x^2 + (7/2)x + 3/4

Exercise 2.3 | Q 1.(vi) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

4x^2 + 5sqrt(2)x - 3

Exercise 2.3 | Q 1.(vii) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

2s^2 - (1 + 2sqrt(2))s + sqrt(2)

Exercise 2.3 | Q 1.(viii) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

v^2 + 4sqrt(3)v - 15

Exercise 2.3 | Q 1.(ix) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

y^2 + 3/2 sqrt(5)y - 5

Exercise 2.3 | Q 1.(x) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

7y^2 - 11/3 y - 2/3

Exercise 2.4 [Pages 14 - 15]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 2 Polynomials Exercise 2.4 [Pages 14 - 15]

Exercise 2.4 | Q 1.(i) | Page 14

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

(-8)/3, 4/3

Exercise 2.4 | Q 1.(ii) | Page 14

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

21/8, 5/16

Exercise 2.4 | Q 1.(iii) | Page 14

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

-2sqrt(3), -9

Exercise 2.4 | Q 1.(iv) | Page 14

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

(-3)/(2sqrt(5)), -1/2

Exercise 2.4 | Q 2 | Page 14

Given that the zeroes of the cubic polynomial x3 – 6x2 + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.

Exercise 2.4 | Q 3 | Page 15

Given that sqrt(2) is a zero of the cubic polynomial 6x^3 + sqrt(2)x^2 - 10x - 4sqrt(2), find its other two zeroes.

Exercise 2.4 | Q 4 | Page 15

Find k so that x2 + 2x + k is a factor of 2x4 + x3 – 14 x2 + 5x + 6. Also find all the zeroes of the two polynomials.

Exercise 2.4 | Q 5 | Page 15

Given that x - sqrt(5) is a factor of the cubic polynomial x^3 - 3sqrt(5)x^2 + 13x - 3sqrt(5), find all the zeroes of the polynomial.

Exercise 2.4 | Q 6 | Page 15

For which values of a and b, are the zeroes of q(x) = x3 + 2x2 + a also the zeroes of the polynomial p(x) = x5 – x4 – 4x3 + 3x2 + 3x + b? Which zeroes of p(x) are not the zeroes of q(x)?

## Chapter 2: Polynomials

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4

## NCERT solutions for Mathematics Exemplar Class 10 chapter 2 - Polynomials

NCERT solutions for Mathematics Exemplar Class 10 chapter 2 (Polynomials) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Exemplar Class 10 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Exemplar Class 10 chapter 2 Polynomials are Geometrical Meaning of the Zeroes of a Polynomial, Relationship Between Zeroes and Coefficients of a Polynomial, Division Algorithm for Polynomials, Concept of Polynomials, Concept of Polynomials.

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