# NCERT Exemplar Class 10 Maths Chapter 4 Solutions: Quadratic Equations

NCERT Exemplar Class 10 Maths Solutions for Chapter 4 ‘Quadratic Equations’ are made to fulfil your requirement of guidance during self-study. In the NCERT Exemplar Maths Class 10 exercise questions, you will be introduced to quadratic equations and the methods to find quadratic roots. You will get to practice the three methods of finding roots – factorization, completing the square and the quadratic formula. Also, you will learn to calculate the type of roots beforehand using the discriminant of the quadratic equation.

Chapter 4 comprises 4 exercises with 28 questions categorized systematically. By solving the questions, you will be able to solve different practical problems of daily life and will also learn to quickly decipher the mathematical context of statement-based questions from your syllabus. These questions are varying in nature and are based on the latest CBSE Class 10 exam pattern.

The NCERT Class 10 Maths Exemplar problems with solutions provided by Instasolv are analytical and detailed in nature. We understand the importance of self-study and therefore we have compiled all answers in such a manner that will be ideal for online guidance. The solutions written by our experts comply with the latest guidelines given by CBSE.

## Important Topics for NCERT Exemplar Class 10 Maths Solutions Chapter 4: Quadratic Equations

**Introduction to Quadratic Equations:**

An equation having a single variable, say x, and the degree 2 is termed as a quadratic equation. It is expressed as ax^{2}+bx+c=0. Here a, b and c are real numbers and a≠0.

Roots of this quadratic equation are equal to the zeroes of the polynomial p(x)=ax^{2}+bx+c, that is, If is the root, then aα^{2}+bα+c=0

**Roots of Quadratic Equation by Factorisation Method**

- The first step is to factorize the quadratic polynomial.
- After that, to find the roots, we will equate each linear factor of the polynomial to 0, thus, getting a value of x for each.
- These values are the roots that are needed.

**Roots of Quadratic Equation by Completing Squares**

- Firstly, we add and subtract a desirable constant number to the equation.
- The second step is to club the terms of x
^{2}and x in such a way that we can write it as complete squares. - We can now complete the squares and evaluate the value of x.

**Quadratic Formula**

If we consider the quadratic equation as ax^{2}+bx+c=0, then the value of x as the root of the equation can be given such that,

Here, we call the term b^{2}-2ac as the Discriminant which is denoted by D.

Therefore D = b^{2}-2ac. This value is of great significance in determining the type of roots of a given quadratic equation.

**Types and Existence of Roots of a Quadratic Equation**

**If b**^{2}-2ac ≥0, there exist two different and real roots.- If b
^{2}-2ac =0, there exist two equal real roots. - If b
^{2}-2ac ≤0, there exist no roots.

### Exercise Discussion of NCERT Exemplar Class 10 Maths Solutions Chapter 4: Quadratic Equations

- Solving exercise 4.1 will help you learn how to evaluate multiple-choice questions on quadratic equations.
- Exercise 4.2 consists of mainly short answer type questions on types of roots of quadratic equations.
- Exercise 4.3 also consists of short answer type questions where you have to find roots of quadratic equations using the factorization method and using the quadratic formula. These questions will require you to apply detailed knowledge.
- Exercise 4.4 is the most important and conceptual exercise. The exercise solutions are of long answer type in this exercise. This exercise also consists of some most recurring questions from your exam.
- It is advised that you practice the exercises in the exemplar chapter in a detailed way. This will help you in your CBSE board exams and other important exams such as National Talent Search Exam, etc.

### Why use NCERT Exemplar Class 10 Maths Solutions Chapter 4 by Instasolv?

- You can easily rely on the solutions for Class 10 NCERT Exemplar problems for Chapter 4 by Instasolv as they are ideal for self-study. All the exercise questions have been covered by us.
- The experts at Instasolv continuously update themselves to keep track of any doubts you might incur while studying. Hence, you will find answers to all your queries here.

To score well in the exam, you should only look up to NCERT Solutions and NCERT Exemplar Class 10 Maths Solutions as they are self-sufficient and covers the entire syllabus of CBSE.