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# 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

An equation having a single variable, say x, and the degree 2 is termed as a quadratic equation. It is expressed as ax2+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)=ax2+bx+c, that is, If is the root, then aα2+bα+c=0

Roots of Quadratic Equation by Factorisation Method

1. The first step is to factorize the quadratic polynomial.
2. 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.
3. These values are the roots that are needed.

Roots of Quadratic Equation by Completing Squares

1. Firstly, we add and subtract a desirable constant number to the equation.
2. The second step is to club the terms of x2 and x in such a way that we can write it as complete squares.
3. We can now complete the squares and evaluate the value of x.

If we consider the quadratic equation as ax2+bx+c=0, then the value of x as the root of the equation can be given such that, Here, we call the term b2-2ac as the Discriminant which is denoted by D.

Therefore D = b2-2ac. 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 b2-2ac ≥0, there exist two different and real roots.
• If b2-2ac =0, there exist two equal real roots.
• If b2-2ac ≤0, there exist no roots.