# NCERT Solutions for Class 10 Maths Chapter 4 – Quadratic Equations

Our comprehensive** **NCERT Solutions for Class 10 Maths Chapter 4 – Quadratic Equations are carefully crafted by an expert team of mathematics teachers. They cover all significant concepts given in CBSE NCERT Solutions for Class 10 Maths Book. Some of the topics covered in this chapter include the solution of the quadratic equation by factorisation, the solution of the quadratic equation by completing the square, and nature of roots. You get answers to all questions from all the exercises in a step by step manner to facilitate easy learning of complex topics.

The questions given in** **Class 10 Maths Quadratic Equations are related to finding roots of quadratic equations and converting word problems into quadratic equations before solving them. There are a total of 4 exercises at the end of the chapter containing a total of 24 questions. All of these questions have been systematically answered in our Quadratic Equations to help clear your fundamentals and doubts about the topics of this chapter and make your conceptual foundation stronger.

NCERT Solutions for Class 10 Maths Chapter 4 – Quadratic Equations give you ample amount of practice and understanding of the mathematical concepts and methods dealt in NCERT Class 10 Maths Chapter 4. They are just what you need to revise quickly and effectively during class 10 board exams and various competitive exams. Solutions for NCERT CBSE Class 10 Maths Chapter 4 prepare you thoroughly for your board exams.

## NCERT Class 10 Maths Chapter 4: Important Topics

**Introduction**

This part of the 4th chapter of CBSE NCERT 10 Maths book tells you that when we equate the quadratic polynomial of the form *a**x ^{2} + bx*

*+ c, a ≠ 0*to zero, we get a quadratic equation. Quadratic equations are encountered in many real-life situations.

**Quadratic Equations**

Here you will learn that a quadratic equation in the variable *x* is an equation of the form *a**x ^{2} + bx*

*+ c = 0*, where a, b, c are real numbers,

*a ≠ 0*.

For example, *10**x – x ^{2}*

*+ 300 = 0*is a quadratic equation, and

*a*

*x*

^{2}+ bx*+ c = 0, a ≠ 0*is called the standard form of a quadratic equation. Sometimes we need to simplify the given equation of higher degree before deciding whether it is quadratic or not.

**The Solution of a Quadratic Equation by Factorisation**

This part of Class 10 Maths Quadratic Equations teaches you the factorisation method of solving equations. Values of the variable *x* for which a quadratic equation is satisfied are called the roots of the quadratic equation.

Suppose, α is a root or solution of the quadratic equation *a**x ^{2} + bx*

*+ c = 0*, then, a

*α*

^{2}*+ bα + c = 0*. A quadratic equation can have at the most two roots and sometimes may not have any real root. Graphically, the roots of a quadratic equation are the points where the graph of the quadratic polynomial cuts the x-axis.

If we can factorise *a**x ^{2} + bx*

*+ c, a ≠ 0*, into a product of two linear factors, then the roots of the quadratic equation

*a*

*x*

^{2}+ bx*+ c = 0*can be found by equating each factor to zero. This method of solving a quadratic equation is called the factorisation method.

**The Solution of a Quadratic Equation by Completing the Square**

This portion of the NCERT Solutions for Class 10 Maths Chapter 4 tells you that a quadratic equation can also be solved by the method of completing the square like

*(x + a)2 – b ^{2} = 0*

In order to directly obtain the roots of a quadratic equation from the standard form of the equation, we use Quadratic Formula. So, for the quadratic equation *ax ^{2} + bx*

*+ c = 0*, the roots will be given by –

*x* = [- b ± √(b* ^{2}*-4ac)]/2a

provided, b* ^{2}* – 4ac ≥ 0

By substituting the values of a, b and c, we can directly get the roots of the equation.

**Nature of Roots**

NCERT CBSE Class 10 Maths Chapter 4 tells you that a quadratic equation a*x^{2}* + b

*x*+ c = 0 has (i) two distinct real roots, if b

*– 4ac > 0, (ii) two equal roots (i.e., coincident roots), if b*

^{2}*– 4ac = 0, and (iii) no real roots, if b2 – 4ac < 0. Since b*

^{2}*– 4ac determines whether the quadratic equation a*

^{2}*x*2 + b

*x*+ c = 0 has real roots or not, b2 – 4ac is called the discriminant of this quadratic equation.

**NCERT Class 10 Maths Chapter 4 – Quadratic Equations Exercises**

All the questions asked in CBSE NCERT Class 10 Maths Chapter 4 have been solved step by step in NCERT solutions for class 10 Maths Chapter 4 – Quadratic Equations. The solutions give you simple tips and techniques to solve correctly and easily. The components of all the 4 exercises of NCERT Class 10 Maths Chapter 4 are as given below. They comprise a total of 24 questions.

**Exercise 4.1**

This exercise contains 2 questions. Question 1 asks you to check if the given equations are quadratic. Question 2 asks you to convert the given information in the form of a quadratic equation.

**Exercise 4.2 **

This exercise comprises 6 questions. Questions 1 and 2 ask you to provide the roots and solutions of the given quadratic equations. Question 3 to 6 ask you to convert the given information to the quadratic equation and solve them.

**Exercise 4.3**

All the 11 questions given in this exercise ask you to use either method of completing the square or applying the quadratic formula to solve the equations. You need to first form the quadratic equation in case of question 4 to 11 and then solve.** **

**Exercise 4.4 **

This exercise contains 5 questions. Questions 1 and 2 are based on finding the nature of the roots of the given equation. Question no. 3 to 5 ask you to form the quadratic equation first using the given information and then finding the value for variables in an equation.

NCERT Solutions for Class 10 Maths Chapter 4 – Quadratic Equations covers all the topics of this chapter and gives meticulous and detailed answers to all the above questions.