# RD Sharma Class 10 Chapter 8 Solutions (Quadratic Equations)

Our RD Sharma Class 10 Maths Solutions Chapter 8 – Quadratic Equations** **have been compiled in order to help you score good marks in the CBSE Board exams. This is an essential topic of CBSE Class 10 Syllabus, as questions from this topic always find considerable coverage in question papers every year.** **Our RD Sharma Class 10 Maths Solutions Quadratic Equations** **trains you about what quadratic equations** **are, the methods to find the solution of a quadratic equation such as Factorisation and completing the square methods. Here you will also understand the nature of root and applications of quadratic equations in day to day life.

RD Sharma Class 10 Maths Solutions Chapter 8** **cover the various types of questions asked in this Chapter. They cover the determination of quadratic equations, formulation of quadratic equations, various ways of finding zeros or roots of quadratic equations like factorisation, completing the square and using the quadratic formula. There are a total of 13 exercises comprising of 99 questions in this Chapter.

Solutions of RD Sharma Class 10 Maths Chapter 8** **follow all the essential guidelines of this field. They are written in a comprehensive manner to clear all your doubts quickly and help you build a sound conceptual foundation. These Solutions provide a considerable amount of practice and prepare you well for all competitive exams along with Class 10 board exams.

## Class 10 Maths Quadratic Equations

Chapter 8 of RD Sharma Class, 10 Maths Book, teaches you about quadratic equations and how to obtain their Solutions. Here you acquire in-depth knowledge about forming quadratic equations and methods to solve them to obtain their roots. The detailed components of the Chapter are given below.

**Quadratic Equations**

Here you will learn than an equation with the form a*x*2 + b*x* + c = 0, with *x* as the variable and a, b, c as real numbers (where a ≠ 0) is known as a quadratic equation. A quadratic equation is obtained upon equating the quadratic polynomial of the form a*x*2 + b*x* + c, a ≠ 0 to zero. Some equations may be of higher degree and need to be simplified before deciding whether it is quadratic or not. We often come across quadratic equations in real-life situations.

**Solving Quadratic Equation by Factorisation**

This part of the Chapter tells you that the first method of solving a quadratic equation is the factorisation method. Here values of the variable *x* are determined, for which a quadratic equation is satisfied. These particular values of *x* are called the roots of the quadratic equation.

It also tells you that a quadratic equation may possess — maximum of two roots or zero real root. Upon plotting a graph, the roots of a quadratic equation are the points where the quadratic polynomial graph intersects the x-axis. The technique of factorisation for answering a quadratic equation involves factorisation of equation a*x*2 + b*x* + c, a ≠ 0, to obtain a product of two linear factors. Finally, roots of the quadratic equation a*x*2 + b*x* + c = 0 are obtained by equating each factor to zero.

**Solving Quadratic Equation by Completing the Square**

This section teaches you that a quadratic equation can also be solved by the method of completing the square like-

(*x* + a)2 – b2 = 0

You can use the quadratic formula to directly obtain the roots of a quadratic equation from the standard form of the equation. For a quadratic equation present in the form a*x*2 + b*x* + c = 0, the roots are given by *x* = [- b ± √(b2-4ac)]/2a; provided, b2 – 4ac ≥ 0.

Further, you will learn that the roots of the equation are calculated by substituting the given values of a, b and c.

**Nature of Roots**

This part of Cass 10 Maths Quadratic Equations teaches you that values of real roots vary for a quadratic equation of the form a*x*2 + b*x* + c = 0.vWhen b2 – 4ac > 0, then the equation possesses two distinct real roots. In case b2 – 4ac = 0, then the equation has two equal roots (known as coincident roots).

Finally, you will learn that if b2 – 4ac < 0 then there are no real roots for the quadratic equation. The term b2 – 4ac is called the discriminant of given quadratic equation because it determines whether the quadratic equation a*x*2 + b*x* + c = 0 has real roots or not.

### RD Sharma Class 10 Maths Chapter 8 Exercises

The Solutions for Chapter 8 of RD Sharma Solutions for Class 10 Quadratic Equations helps you grasp the topic firmly. Quadratic equations Chapter is one of the important Chapters of Class 10 mathematics. It contains thirteen exercises whose components are discussed below.

**Exercise 8.1**

This exercise has 2 questions. Question 1 asks you to identify quadratic equations. Question 2 asks you to check if the given value satisfies the equations given.

**Exercise 8.2**

This exercise contains 3 questions, and all of them are word problems based on real-life situations, and each one of them asks you to form a quadratic equation following the information given.

**Exercise 8.3**

This exercise contains 30 questions. All of them are direct questions asking you to solve the given equation by factorisation method.

**Exercise 8.4**

All the 5 direct questions of this exercise ask you to find the roots of given quadratic equation using the method of completing the square.

**Exercise 8.5**

This exercise consists of 1 question which asks you to write the discriminants of the given quadratic equations.

**Exercise 8.6**

Question 1 asks to determine the nature of roots for all the given quadratic equations. Question 2 to 5 are based upon the determination of real values of roots for all the given equations. Question 6 to 12 test your skills to determine roots for the given equation along with an applied condition to the problem.

**Exercise 8.7 **

This exercise has 20 questions, and all of them are word problems which ask you to form quadratic equations and then solve them using the methods learnt in the Chapter.

**Exercise 8.8 **

This exercise has 7 questions, and all of them are word problems involving some basic concepts on speed, distance and time. All of these questions test your higher-order thinking skills where you need to first form a quadratic equation and then find its answer.

**Exercise 8.9 **

This exercise has 4 questions, and all of them are word problems based on age calculation. All of these questions test your analytical skills. They need you to first formulate the quadratic equation and then solve to find the answer.

**Exercise 8.10**

This exercise consists of 2 questions which are word problems based on trigonometry and perimeter of a rectangle. Both of them ask you to make the equation first and then find a solution.

**Exercise 8.11**

All the 5 questions are word problems from this exercise and are based on area and perimeter calculations of geometrical figures. All of them need to be transformed to a quadratic equation before finding its solution.

**Exercise 8.12**

This exercise contains 2 questions, and both of them are time frame related word problems, where they need to be converted into** a **quadratic equation before finding their Solutions.

**Exercise 8.13**

This exercise contains 6 questions and all of them are word problems based on miscellaneous topics, where you need to convert the given information into a quadratic equation and then find their Solutions applying the methods learnt in the Chapter.

### Benefits of RD Sharma Class 10 Maths Solutions Chapter 8 – Quadratic Equations

- RD Sharma Class 10 Maths Chapter 8-Quadratic Equations cover all the important points of this Chapter in an exhaustive yet to the point manner.
- The Solutions given include detailed explanations and relevant examples to help you learn efficiently.
- Our Maths Shortcuts help you learn fast and more effectively.
- You will find the solutions easy to understand and remember.
- These cover a wide variety of question so that you can practise enough to get hold of the topic.
- They help you in revising the Class 10 Maths Syllabus thoroughly during Board exams.