#### 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

## 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.

#### Textbook solutions for Class 10

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

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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.

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