Xam Idea Class 10 Maths Chapter 4 Solutions: Quadratic Equations
Xam Idea Class 10 Maths Solutions for Chapter 4 ‘Quadratic Equations’ gives an introduction of quadratic equations and discusses how you will solve the questions in an efficient manner. In this chapter of Xam Idea Solutions, you will learn different methods to find quadratic roots. The three methods that you will learn in the chapter to find quadratic roots are factorization method, completing the square and the quadratic formula. The chapter also discusses the types of roots of a quadratic equation.
The Xam Idea Class 10 Maths Solutions for Quadratic Equations consists of an exercise which is further divided into six sections. There are a total of 57 questions in this chapter. Each exercise section comprises questions which cover all the major concepts of the chapter as per the latest CBSE and NCERT syllabus for Class 10 Maths. Once you study the chapter at its core, you will be able to solve these questions without any hurdles in the exams.
Instasolv provides you with the solution to all your queries in the chapter. The answers provided by Instasolv are highly reliable and are preferred by most of the students. The solutions are explained in such a manner that you develop a stronger base and can fully be prepared for Class 10 board exams. Instasolv helps you gain the confidence to find solutions to all types of questions.
Important Topics For Xam Idea Class 10 Maths Solutions Chapter 4: Quadratic Equations
What are Quadratic Equations?
A quadratic equation is an equation that has a single variable such as Y and a degree 2. The equation is written as
ax2+bx+c = 0
In this equation, a0 and a,b,c are the real numbers.
The roots of this quadratic equation = zeros of a polynomial.
p(x) = ax2+bx+c, i.e if a is said to be the root, then the equation will be aa2+ba+c = 0
Factorisation Method in Quadratic Equations
- In the first step, we start with factoring the quadratic polynomial
- In order to find the roots in the second step, we equate every single linear factor of the polynomial to 0 which gives us the value of x for each.
- Thus, we get the values which are the required roots.
Completing Squares in the Roots of Quadratic Equations
- In the first step, we add and subtract the equation with a desirable constant number.
- Then, we write the terms of x2 and x in a way that can also be written as complete squares.
- Now, we evaluate the value of x, by completing the squares.
The Quadratic Formula
Let’s consider ax2+bx+c = 0 as a quadratic equation, then the value of x can
be given so that
In this, the term b2-2ac is denoted as ‘D’ because we call it as a discriminant term. However, D = b2 – 2ac. The given value is extremely important in quadratic equations to determine the type of roots.
Types of Roots of Quadratic Equations
- There are two different and real roots if b2-2ac0.
- There exist two equal as well as real roots if b2-2ac=0.
- No existence of roots if b2-2ac0.
Exercise Discussion For Xam Idea Class 10 Maths Solutions Chapter 4: Quadratic Equations
Very Short Answer Type Questions
In this set, there are a total number of 6 questions. The questions cover important topics of the chapter like nature of roots. This set of exercise includes questions where you are given the roots of the quadratic equation and you will have to find the value of c. In some questions, you have to predict the nature of roots of given quadratic equations.
Short Answer type-I
There are a total of 12 questions in this section in which you have to solve the equations as given in the questions in order to justify your answer. Also, there are few questions in which you have to find the value of k in the given equations. These questions are framed like- is 0.3 a root of the given equation? justify or find the value of k in the equation.
Short Answer Type-II
There are a total number of 17 questions in this section. In these questions, you are required to find the roots of the given quadratic equations. You are required to use the different methods of finding roots of an equation such as the substitution method and the prime factorization method.
Long Answer Type Questions
In the long question section, there are 20 questions overall. In these questions, you will need to solve the equations using the quadratic formula and also there are some questions in which you need to find the number of the given difference. In some questions, you are given the difference between two numbers and their reciprocals and you have to find the numbers or solve the equation for x using the quadratic formula.
Higher Order Thinking Skills
There are only 4 questions in this section. The questions are framed in such a way that you are required to find effective solutions to the complex questions. These questions are based on complex thinking and you will face questions related to pipes and cisterns. These kind of questions are very important from competitive exams point of view.
This section contains 15 questions in all. The questions are based on general values. For instance, there are questions related to work done where you are given the number of days two people take to do work individually and you have to find the number of days they would take to do the same piece of work together. There are also questions related to the efficiency of the work done.
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