#### Chapters

Chapter 2: Polynomials

Chapter 3: Pair of Linear Equations in Two Variables

Chapter 4: Quadratic Equations

Chapter 5: Arithmetic Progressions

Chapter 6: Triangles

Chapter 7: Coordinate Geometry

Chapter 8: Introduction to Trigonometry

Chapter 9: Some Applications of Trigonometry

Chapter 10: Circles

Chapter 11: Constructions

Chapter 12: Areas Related to Circles

Chapter 13: Surface Areas and Volumes

Chapter 14: Statistics

Chapter 15: Probability

#### NCERT Mathematics Class 10

## Chapter 2: Polynomials

#### Chapter 2: Polynomials Exercise 2.10 solutions [Page 28]

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x), in the following.

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x)

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x)

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x)

#### Chapter 2: Polynomials Exercise 2.20 solutions [Page 33]

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

x^{2} – 2x – 8

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

4s^{2} – 4s + 1

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

6x^{2} – 3 – 7x

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

4u^{2} + 8u

t^{2} – 15

3x^{2} – x – 4

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

`1/4 , -1`

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

`sqrt2 , 1/3`

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

`0, sqrt5`

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

1, 1

`-1/4 ,1/4`

4, 1

#### Chapter 2: Polynomials Exercise 2.30 solutions [Page 36]

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following

p(x) = x^{3} – 3x^{2} + 5x – 3, g(x) = x^{2} – 2

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following : p(x) = x^{4} – 3x^{2} + 4x + 5, g(x) = x^{2} + 1 – x

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following

p(x) = x^{4} – 5x + 6, g(x) = 2 – x^{2}

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial

t^{2} – 3, 2t^{4} + 3t^{3} – 2t^{2} – 9t – 12

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial

x^{2} + 3x + 1, 3x^{4} + 5x^{3} – 7x^{2} + 2x + 2

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial

x^{3} – 3x + 1, x^{5} – 4x^{3} + x^{2} + 3x + 1

Obtain all other zeroes of 3x^{4} + 6x^{3} – 2x^{2} – 10x – 5, if two of its zeroes are `sqrt(5/3)` and - `sqrt(5/3)`

On dividing x^{3} – 3x^{2} + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4, respectively. Find g(x)

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm

deg p(x) = deg q(x)

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm

deg q(x) = deg r(x)

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm

deg r(x) = 0

#### Chapter 2: Polynomials Exercise 2.40 solutions [Pages 36 - 37]

Verify that the numbers given along side of the cubic polynomials are their zeroes. Also verify the relationship between the zeroes and the coefficients.

`2x^3 + x^2 – 5x + 2 ; 1/2, 1, – 2`

Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case

x^{3} – 4x^{2} + 5x – 2; 2, 1, 1

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, − 7, − 14 respectively

If the zeroes of the polynomial x^{3} – 3x^{2} + x + 1 are a – b, a, a + b, find a and b

If two zeroes of the polynomial x^{4} – 6x^{3} – 26x^{2} + 138x – 35 are 2 ± `sqrt3` , find other zeroes

If the polynomial x^{4} – 6x^{3} + 16x^{2} – 25x + 10 is divided by another polynomial x^{2} – 2x + k, the remainder comes out to be x + a, find k and a.

## Chapter 2: Polynomials

#### NCERT Mathematics Class 10

#### Textbook solutions for Class 10

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

NCERT solutions for Class 10 Maths 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 Textbook for Class 10 solutions in a manner that help students grasp basic concepts better and faster.

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

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