#### 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

#### 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 each case

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)

#### 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 quadratic polynomial x^{2} – 2x – 8 and verify a relationship between zeroes and its coefficients

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

#### 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

#### 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.

#### Extra questions

Find the zeros of the quadratic polynomial 9x^{2} - 5 and verify the relation between the zeros and its coefficients.

Find the zeros of the quadratic polynomial 6x^{2} - 13x + 6 and verify the relation between the zero and its coefficients.

if α and β are the zeros of ax^{2} + bx + c, a ≠ 0 then verify the relation between zeros and its cofficients

Prove relation between the zeros and the coefficient of the quadratic polynomial ax^{2} + bx + c

Find the zeros of the quadratic polynomial 4x^{2} - 9 and verify the relation between the zeros and its coffiecents.

#### 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.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

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

Using NCERT Class 10 solutions Polynomials exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 10 prefer NCERT Textbook Solutions to score more in exam.

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