# NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.1

NCERT Solutions for class 10 Maths chapter 4 Exercise 4.1 (Class 10 Ex. 4.1) Quadratic Equations View in Video Format with Hindi Medium and English Medium. You can download these CBSE NCERT Solutions in PDF format for academic session 2021-22. Uttar Pradesh Madhyamik Shiksha Parishad, Prayagraj also implemented NCERT Books as a course books for academic session 2021-2022. So UP Board High School students can take benefits of these solutions free of cost. Download UP Board Solution for Class 10 Maths Exercise 4.1 in Hindi Medium. All the solutions are applicable for CBSE Board as well as UP Board and Uttarakhand Board students who are using NCERT Books for 2021-2022.

Download Class 10 Online and Offline Apps and CBSE Solutions of other subjects for offline use updated for academic session 2021-22.## NCERT Solutions for class 10 Maths chapter 4 Exercise 4.1

Class: 10 | Maths (English and Hindi Medium) |

Chapter 4: | Exercise 4.1 |

### 10 Maths Chapter 4 Exercise 4.1 Solutions

CBSE NCERT Solutions for class 10 Maths chapter 4 Exercise 4.1 Quadratic Equations all question-answers in English as well as Hindi Medium to use online or download in PDF are given below. If you need Chapter 4 Exercise 4.1 in Hindi Medium offline use, just download in PDF or download Offline apps. All solutions are updated as per the suggestions received by students/teachers/parents based on latest CBSE Syllabus 2021-2022. These solutions are available do download (Exercise 4.1) in PDF form. Download Class 10 Maths App as well as Kaksha 10 Ganit App for offline use.

#### Class 10 Maths Chapter 4 Exercise 4.1 Solution in Videos

#### Important Terms Related to Quadratic Equations

- Quadratic Equation: An equation of the form ax² + bx + c = 0, a ≠ 0 is called a quadratic equation in one variable x, where a, b and c are constants. For example 2 x² – 3x + 1 = 0
- Roots of a Quadratic Equation: Let ax² + bx + c = 0, be a quadratic equation. If α is a root of this equation. It means x = α satisfies this equation i.e., aα² + bα+ c = 0.
- Discriminant: For the quadratic equation ax² + bx + c = 0 the expression is called the discriminant and denoted by D. Then the roots of the quadratic equation are given by (–b ± √D)/2a.

##### Points to be Remembered

- Number of Roots: A quadratic equation has two roots, one roots or no roots, it is depending the value of D.

1. If D > 0, it has two distinct real roots.

2. If D = 0, it has two equal roots.

3. If D < 0, there is no real roots. - Methods for Solving Quadratic Equation

1. By factorization

2. By completing the square

3. By Quadratic Formula - Quadratic Formula to find roots of ax² + bx + c = 0 is given by x = (– b – √D)/2a and x = (– b + √D)/2a.

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### Important Questions of 10th Maths Exercise 4.1

##### Check whether the following are quadratic equations: (x – 2)² + 1 = 2x – 3

LHS = (x – 2)2 + 1 = x2 – 4x + 4 + 1 = x2 – 4x + 5

Therefore, (x – 2)² + 1 = 2x – 3 can be rewritten as

x² – 4x + 5 = 2x – 3

i.e., x² – 6x + 8 = 0

It is of the form ax² + bx + c = 0.

Therefore, the given equation is a quadratic equation.

##### What is the relation between zeros of a quadratic polynomial and roots of a quadratic equation?

The zeroes of the quadratic polynomial ax2 + bx + c and the roots of the quadratic equation ax2 + bx + c = 0 are the same.

##### How can we check an equation is whether quadratic or not?

After the simplification, write the equation in standard format. If the maximum power of the variable is 2 and all powers are in whole numbers, the equation is quadratic equation.

##### What is discriminant in a quadratic equation?

b² – 4ac determines whether the quadratic equation ax² + bx + c = 0 has real roots or not, b² – 4ac is called the discriminant of this quadratic equation.

##### What is the standard form of quadratic equation in 10th Maths Ex. 4.1?

A quadratic equation in the variable x is an equation of the form ax² + bx + c = 0, where a, b, c are real numbers, a ≠ 0. For example, 2x² + x – 300 = 0 is a quadratic equation. Similarly, 2x² – 3x + 1 = 0, 4x – 3x² + 2 = 0 and 1 – x² + 300 = 0 are also quadratic equations. In fact, any equation of the form p(x) = 0, where p(x) is a polynomial of degree 2, is a quadratic equation. When we write the terms of p(x) in descending order of their degrees, then we get the standard form of the quadratic equation. That is, ax² + bx + c = 0, a ≠ 0 is called the standard form of a quadratic equation.

##### What type of questions students will solve in exercise 4.1 of 10th Maths?

There are 2 questions in exercise 4.1 (chapter 4 Quadratic equations) of class 10 mathematics. In first question students have to check whether the given equation is quadratic or not.

Example of first question:

Check whether the following are quadratic equations:

(x – 2)(x + 1) = (x – 1)(x + 3) (ii) (x – 3)(2x +1) = x(x + 5)

In second question students have to represent the given situation in the form of quadratic equation.

Example of situation: 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.

##### Which question of exercise 4.1 class 10th Maths are easy to solve?

Students can easily do Q1 of exercise 4.1 (chapter 4 Quadratic equations) of class 10th mathematics.

##### Which question of exercise 4.1 of class 10th Maths, students find difficult and why?

Students find Q2 of exercise 4.1 (chapter 4 Quadratic equations) of class 10th mathematics difficult because Q2 contains 4 word problems and generally students think word problems are difficult to solve.