RS Aggarwal Class 10 Chapter 4 Solutions (Quadratic Equations)
RS Aggarwal Solutions for Class 10 Chapter 4 are prepared to help you prepare for class 10 board exams easily. This chapter of RS Aggarwal Class 10 Maths Solutions is about the standard form of quadratic equations, roots of quadratic equations, types of roots of quadratic equations, various methods to identify the quadratic equations and applicability of quadratic equations in real life.
The chapter consists of 6 exercises with a total of 273 questions. The exercise questions of this chapter are all about solving the quadratic equations. Some of the questions demand to solve the quadratic equations by the method of completing the square and while in others you are required to apply factorisation. This chapter will also help you learn how to find out if an equation has no real roots. In a few questions, you have to find the discriminant of the equation. The chapter also covers the topic of the comparison of a given equation and the general quadratic equation.
Our RS Aggarwal Class 10 Maths solutions would allow you to get a thorough understanding of quadratic equations. You will be able to secure good marks in your exams as well as you will be able to apply the knowledge of quadratic equations in day to day life. Depicting the area of a certain plot, measuring speed are the real-life examples where quadratic equations.
Important Topics for RS Aggarwal Class 10 Solutions for Chapter 4: Quadratic Equations
The standard form of a quadratic equation is a2+bx + c = 0.
where, a≠0, a,b,c are known numbers and x is unknown.
When an equation is considered as Quadratic?
- For any equation to be quadratic, it is mandatory to have at least one squared variable.
- The quadratic equation is an equation of second degree.
- If an equation is a fraction, then it will not be considered as a quadratic equation.
Factorisation method is used to solve the quadratic equation and it follows by splitting the middle term of the equation and then proceeding with finding the roots of the equation. Also, it is seen that almost two roots are possible in the quadratic equation. Generally, α is called as a root of the quadratic equation.
For instance, in equation 4x2+ 7x+3=0, by applying factorisation we get, 4x2+4x+3x+3. (7x is split into 4x+3x)
Completing the Square method
When an equation is not possible to solve by factorisation method, one is bound to go for completing the square method.
Under this, the equation is solved by taking the square roots.
For instance, in equation x2= 16, we get x=4 and x= (-4)
Nature of roots
An equation comprises one of the roots. They can be real, equal or distinct, or no real roots.
The discriminant formula is used to identify the nature of roots of any equation.
The formula is D= b2– 4ac
- When D is greater than 0, the roots of the equation are real and unequal.
- When D is equal to 0, the roots of the equation are real and equal.
- When D is negative, the roots of the equation have no real roots.
After finding out the nature of the roots, you are asked to find the roots of the given equation.
It is possible with the help of formula, which is
Exercise Discussion for RS Aggarwal Solutions for Class 10 Chapter 4: Quadratic Equations
- Initially, the first exercise has some basic questions of solving a quadratic equation. Also, the value of roots is asked in this exercise.
- The second exercise is all about solving the equation by applying the completing square method. There is no formula in this method but as we solve step by step, the solution gets nearer.
- In the third exercise, there are questions where you will need the quadratic formula. This is required to solve the discriminant of the equation.
- Ultimately, every equation is needed to be solved either by applying the factorisation method, quadratic method or completing the square method.
- In the fifth exercise, questions of identifying the nature of roots are asked. Additionally, according to the conditions, questions are asked to find the required integer, multiples or natural number.
- In the last exercise, you will solve the product of roots, find the nature of roots of the equation, find the value of p and also identify the equation if it’s quadratic or not.
Benefits of RS Aggarwal Solutions for Class 10 Chapter 4: Quadratic Equations
- One of the major benefits of RS Aggarwal Solutions for Class 10 book is that the chapter of the quadratic equation is explained in the possible simpler way. This enables you to get the concept in just a single glance.
- The quadratic equation is the easiest chapter in the CBSE Class 10 Maths syllabus. You can take the advantage to score higher in examinations by preparing the chapter well with the help of our solutions.
- We have included clear explanations and stepwise answers to ensure that you understand the concepts of the chapter completely.
- We adhere to the latest CBSE guidelines while formulating the solutions.