NCERT Solutions for class 10 Maths chapter 4 Exercise 4.1 in Hindi and English Medium updated for CBSE board 2024-25 examination. Grade 10 Math exercise 4.1 contains the basic questions of quadratic equations to convert into standard format.

• ## Class 10 Maths Exercise 4.1 Solutions

 Class: 10 Mathematics Chapter 4: Exercise 4.1 Contents: NCERT Textbook Question Answers Mode of Content: Text, Images and Videos Session: CBSE 2024-25 Medium: English and Hindi Medium

### NCERT Solutions for class 10 Maths chapter 4 Exercise 4.1

Class 10 Math Ex. 4.1 solution 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 2024-25. Uttar Pradesh Madhyamik Shiksha Parishad, Prayagraj also implemented NCERT Books as a course books for academic session 2024-25. 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 2024-25. Download Class 10 Solution App and CBSE Solutions of other subjects for offline use updated for academic session 2024-25.

### 10 Maths Chapter 4 Exercise 4.1 Solutions

#### Important Terms Related to Quadratic Equations

1. 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
2. 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.
3. 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
• Quadratic Formula to find roots of ax² + bx + c = 0 is given by x = (– b – √D)/2a and x = (– b + √D)/2a.

### 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.

Download NCERT Books and Offline Apps 2024-25 based on new CBSE Syllabus. Ask your doubts related to NIOS or CBSE Board and share your knowledge with your friends and other users through Discussion Forum.

### 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.

Last Edited: May 18, 2024