#### 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 4 - Quadratic Equations

#### Pages 73 - 74

Check whether the following is the quadratic equations : (x + 1)^{2} = 2(x - 3)

Check whether the following is the quadratic equations: x^{2} - 2x = (-2)(3 - x)

Check whether the following is the quadratic equations: (x - 2)(x + 1) = (x - 1)(x + 3)

Check whether the following is the quadratic equations (*x* - 3)(2*x* + 1) = *x*(*x* + 5)

Check whether the following is the quadratic equations: (2x - 1)(x - 3) = (x + 5)(x - 1)

Check whether the following is the quadratic equations : x^{2} + 3x + 1 = (x - 2)^{2}

Check whether the following is the quadratic equations: (x + 2)^{3} = 2x(x^{2} - 1)

Check whether the following is the quadratic equations: x^{3} - 4x^{2} - x + 1 = (x - 2)^{3}

Represent the following situations in the form of quadratic equations

The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot

Represent the following situations in the form of quadratic equations

The product of two consecutive positive integers is 306. We need to find the integers.

Represent the following situations in the form of quadratic equations

Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan's present age.

Represent the following situations in the form of quadratic equations.

A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

#### Page 76

Find the roots of the following quadratic equations by factorisation *x*^{2} – 3*x* – 10 = 0

Find the roots of the following quadratic equations by factorisation 2*x*^{2} + *x* – 6 = 0

Find the roots of the following quadratic equations by factorisation

`sqrt2 x^2 + 7x + 5sqrt2 = 0`

Find the roots of the following quadratic equations by factorisation `2x^2 – x + 1/8 = 0`

Find the roots of the following quadratic equations by factorisation: 100x^{2} – 20x + 1 = 0

Find two numbers whose sum is 27 and product is 182.

Find two consecutive positive integers, sum of whose squares is 365

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.

#### Pages 87 - 88

Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x^{2} – 7x + 3 = 0

Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2*x*^{2} + *x* – 4 = 0

Find the roots of the following quadratic equations, if they exist, by the method of completing the square `4x^2 + 4sqrt3x + 3 = 0`

Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2*x*^{2} + *x* + 4 = 0

Find the roots of the quadratic equations 2x^{2} – 7x + 3 = 0 by applying the quadratic formula.

Find the roots of the quadratic equations 2x^{2} + x – 4 = 0 by applying the quadratic formula.

Find the roots of the quadratic equations `4x^2+4sqrt3x + 3 = 0` by applying the quadratic formula.

Find the roots of the quadratic equations 2*x*^{2} + *x* + 4 = 0 by applying the quadratic formula.

Find the roots of the following equations:

`x-1/x = 3, x ≠ 0`

Find the roots of the following equations

`1/(x+4) - 1/(x-7) = 11/30, x = -4, 7`

The sum of the reciprocals of Rehman's ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age.

In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects

The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Two water taps together can fill a tank in `9`hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, find the average speed of the two trains.

Sum of the areas of two squares is 468 m^{2}. If the difference of their perimeters is 24 m, find the sides of the two squares.

#### Page 91

Find the nature of the roots of the following quadratic equation. If the real roots exist, find them

2x^{2} - 3x + 5 = 0

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them;

`3x^2 - 4sqrt3x + 4 = 0`

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them

2*x*^{2} - 6*x* + 3 = 0

Find the values of *k* for each of the following quadratic equations, so that they have two equal roots. 2*x*^{2} + *kx* + 3 = 0

Find the values of *k* for each of the following quadratic equations, so that they have two equal roots.

kx (x - 2) + 6 = 0

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m^{2}? If so, find its length and breadth.

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth

#### Extra questions

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.

Find the roots of the quadratic equation 4x^{2} + 4√3x + 3 = 0

Find the roots of the quadratic equation 2x^{2} + x + 4 = 0

Without solving, examine the nature of roots of the equation 2x^{2} – 7x + 3 = 0

For what value of m, are the roots of the equation (3m + 1)x^{2} + (11 + m) x + 9 = 0 equal?

Without solving, examine the nature of roots of the equation 4x^{2} – 4x + 1 = 0

Without solving, examine the nature of roots of the equation x^{2} – 5x – 2 = 0

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with

Solve the following quadratic equations

(i) 7x^{2} = 8 – 10x

(ii) 3(x^{2} – 4) = 5x

(iii) x(x + 1) + (x + 2) (x + 3) = 42

Solve the following quadratic equations

(i) x^{2} + 5x = 0 (ii) x^{2} = 3x (iii) x^{2} = 4

Without solving, examine the nature of roots of the equation 2x^{2} + 2x + 3 = 0

Solve for x : 12abx^{2} – (9a^{2} – 8b^{2} ) x – 6ab = 0

Solve (i) x^{2} + 3x – 18 = 0

(ii) (x – 4) (5x + 2) = 0

(iii) 2x^{2} + ax – a2 = 0; where ‘a’ is a real number

#### Textbook solutions for Class 10

## NCERT solutions for Class 10 Mathematics chapter 4 - Quadratic Equations

NCERT solutions for Class 10 Mathematics chapter 4 (Quadratic Equations) include all questions with solution and detail explanation from Mathematics Textbook for Class 10. 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 created 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 4 Quadratic Equations are Quadratic Equations, Nature of Roots, Relationship Between Discriminant and Nature of Roots, Solutions of Quadratic Equations by Factorization, Solutions of Quadratic Equations by Completing the Square, Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated, Quadratic Equations Examples and Solutions.

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