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RS Aggarwal - Class 10 Solutions for Quadratic Equations

Q: 1. What is Discriminant?

The term (b2 - 4ac) that is present in the quadratic formula is considered as the discriminant of a quadratic equation. To find out the nature of roots, a student is required to find out the discriminant of a particular equation. The discriminant is responsible for revealing the nature of roots. The nature of roots can get divided into two types which are real and imaginary roots.

RS Aggarwal Solutions

RS Aggarwal - Class 10 Solutions for Quadratic Equations

Quadratic Equations Solutions for RS Aggarwal Class 10 - Chapter 10

Maths being an important subject, it is essential to understand the concepts of every chapter. RS Aggarwal Class 10 - Chapter 10 Quadratic Equation is considered to be one of the most challenging chapters that students have to prepare for exams. To make this preparation furthermore straightforward, students can take guidance from Vedantu's RS Aggarwal Solutions Class 10 - Chapter 4 Quadratic Equations.

This Solution will play the role of an advisor and a teacher for students. These solutions are highly recommended for those students who face trouble in solving quadratic equation problems. Every NCERT Solution is provided to make the study simple and interesting on Vedantu. Subjects like Science, Maths, English become easy to study if you have access to NCERT Solution for Class 10 Science, Maths solutions and other subjects. You can also download NCERT Solutions for Class 10 Maths to help you to revise the complete syllabus and score more marks in your examinations.

RS Aggarwal Solutions for Class 10 Maths - Chapter 10

We have provided step-by-step Solutions for all exercise questions given in the PDF of Class 10 RS Aggarwal Chapter 10 - Quadratic Equations. All the Exercise questions with solutions in Chapter 10 - Quadratic Equations are given below:

Exercise (Ex 10A) 10.1

Exercise (Ex 10B) 10.2

Exercise (Ex 10C) 10.3

Exercise (Ex 10D) 10.4

Exercise (Ex 10E) 10.5

Exercise (Ex 10F) 10.6

Exercise (Ex 10G) 10.7

Exercise (Ex 10H) 10.8

Quadratic Equation Class 10 RS Aggarwal Solutions - FREE PDF Download

To avoid finding it difficult to understand the concepts and formulas of this subject, students must start practising the problems on a daily basis beforehand while referring to RS Aggarwal Solutions Class 10 Chapter 4 Quadratic Equations - Ex 4A, which is available in a PDF format on Vedantu's site. This PDF will give students a detailed overview of the chapter. Students will gain knowledge on different concepts of a Quadratic Equation such as:

Meaning of Quadratic Equations

Quadratic equations are considered the polynomial equations of degree 2 in one variable if type f(x) = ax2 + bx + c where a, b, c belong to (∈) R and a ≠ 0. This is considered as the general form of a quadratic equation where 'a' is referred to as the leading coefficient, and 'c' is known to be the absolute term of f(x). The values of x that are responsible for satisfying the quadratic equation are known as the roots of the quadratic equation (a,b). The quadratic equation will always have two roots. The nature of roots might be real or imaginary.

Roots of Quadratic Equation

The values of the variables that are satisfying the requirements of a particular quadratic equation are known as roots. In other words, x = a is considered as one of the roots of the quadratic equation f(x), if f(a) = 0.

The real roots of the equation f(x) = 0 are termed as the x-coordinates of the points; this is the point where the curve y = f(x) intersects the x-axis.

It is proved that one of the roots of the quadratic equation is zero whereas the other is equal to -b/a if c = 0.
In case, b = c = 0 then both the roots are measured to be zero.
When a = c, the roots are reciprocal to each other.

Nature of Roots of Quadratic Equation

If the value of the discriminant = 0 i.e. b2 - 4ac = 0	In this case, the quadratic equation will have equal roots i.e. a = b = -b / 2a
If the value of discriminant < 0 i.e. b2 - 4ac < 0	In this case, the quadratic equations will have imaginary roots i.e. a = (p + iq) and b = (p - iq). Where ‘iq’ is considered as the imaginary part of a complex number.
If the value of the discriminant (D) > 0 i.e. b2 - 4ac > 0	In this case, the quadratic equations will have real roots.
If the value of the discriminant > 0 and D is found to be a perfect square.	In this case, the quadratic equation is going to have rational roots.
If the value of the discriminant > 0 and D is not a perfect square.	In this case, the quadratic equation is going to have irrational roots i.e. a = (p + √q) and b = (p - √q)
If the value of the discriminant > 0 and D is found to be a perfect square. Here, a = 1 and b & c are integers	In this case, the quadratic equation is going to have integral roots.

Importance of RS Aggarwal Solutions Class 10 - Chapter 4 Quadratic Equations

This is a challenging chapter with difficult concepts and formulas. Students should, therefore, seek help from Quadratic Equation Class 10 RS Aggarwal Solutions. Some benefits of these Solutions are:

The solutions are explained simply to make it easy for students to understand.
The solutions are prepared by expert teachers who have years of experience in the field.
The solutions are prepared following the rules and regulations imposed by the board.

Sample Question Paper

RS Aggarwal provides you with solutions in a better manner, and additionally explains step-wise-step solutions to problematic queries, thus, making Mathematics interesting for all – particularly the weaker students. Specialists suggest RS Aggarwal's Solutions as it provides easier and faster answers for every question which leaves no topic for later, therefore, the student gets extended time for revision as RS Aggarwal helps in covering the chapters quicker.

They provide solutions for each question in an exceedingly informative manner as the experts want every student to know the key concepts. Regular practice and studying with the assistance of RS Aggarwal's solutions can help in the advance of your speed and efficiency, and accuracy to ace your examination preparation and helps in achieving better and higher scores. Get the PDF copy, RS Aggarwal Class 10 Solutions - Quadratic Equations from the Vedantu website.

Experts at Vedantu have simply and properly defined each question from the beginner level, in a manner that students understand it on their own and do not find it boring. Vedantu provides free access to the RS Aggarwal Class 10 Maths Solutions. You can visit the official website of the Vedantu and click on the link then ‘Download PDF’.

Quadratic Equations

Polynomial equations holding degree 2 in one variable if type f(x) = ax2 + bx + c wherever a, b, c belong to (∈) R and a ≠ 0 are known as Quadratic Equations. It's called the general form of an equation where ‘a’ is referred to as the leading coefficient, and ‘c’ is understood to be the absolute term of f(x).

The values of x that are liable for satisfying the quadratic equation are called the roots of the quadratic equation (a,b). The quadratic equation can invariably have either two roots - real or imaginary.

Quadratic Equations and Its Roots

Roots can be defined as the values of the variables that satisfy the requirements of a given equation. x = a is said to be the roots of the quadratic equation f(x), if f(a) = 0.

The real roots of the equation f(x) = 0 can be said so because of the x-coordinates of the points; the point where the curve y = f(x) intersects the x-axis.

It's proved that one of the roots of the quadratic equation is zero whereas the opposite is equal to -b/a if c = 0.

In case, b = c = 0 then, each of the roots is measured to be zero.

Once a = c, the roots are reciprocal to one another.

Nature of the Roots of Quadratic Equations

If the value of the discriminant is equal to 0 i.e. b2 – 4ac = 0

In this case, the quadratic equation will have equal roots i.e. a = b = -b / 2a

If the value of discriminant < 0 xss=removed xss=removed> 0 i.e. b2 – 4ac > 0

In this case, the quadratic equations will have real roots.

If the worth of the discriminant > 0 and D is found to be a perfect square.

In this case, the quadratic equation can have rational roots.

If the value of the discriminant is greater than 0 and D isn't a perfect square.

In this case, the quadratic equation can have irrational roots i.e. a = (p + √q) and b = (p – √q)

If the value of the discriminant is greater than 0 and D is found to be a perfect square.

Here, a = 1 and b & c can be termed as integers.

In this case, the quadratic equation goes to have integral roots.

FAQs on RS Aggarwal - Class 10 Solutions for Quadratic Equations

1. What is Discriminant?

The term (b² - 4ac) that is present in the quadratic formula is considered as the discriminant of a quadratic equation. To find out the nature of roots, a student is required to find out the discriminant of a particular equation. The discriminant is responsible for revealing the nature of roots. The nature of roots can get divided into two types which are real and imaginary roots.

2. What is a Biquadratic Equation?

The biquadratic equation is considered a polynomial equation with a degree four with no signs of degree three and degree one. To solve a biquadratic equation, you must first convert the equation into quadratic form then you can solve the equation easily with no difficulties.

3. What are the Steps that are Followed While Factoring a Quadratic Equation?

The following steps can get followed for solving a quadratic equation using the factoring method:

Firstly, move all the terms on one side of the equal sign so that all the terms are on one side and zero is on the other side.
Next step is to set each factor as zero.
It is mandatory to solve each equation in order to get the roots.
After getting the roots, put it on the original equation to get the answer.

4. How to download RS Aggarwal Class 10 Solutions - Quadratic Equations?

RS Aggarwal Class 10 Solutions - Quadratic Equations is a vital supply of knowledge that helps in providing students with updated information and is supplementary to the syllabus. RS Aggarwal has one of the most important contributions for students and that is to explain the solutions of the problems in the simplest manner. This simple feature helps the student to cover his chapters quickly and which in turn helps them have a better grasp of the syllabus. Teachers also suggest RS Aggarwal after seeing the improvement in the performance of the weaker and average students. Vedantu provides free access to the RS Aggarwal Class 10 Solutions - Quadratic Equations. On visiting Vedantu, click on the link and then on "Download PDF". You will receive the study material in PDF format. RS Aggarwal Class 10 Solutions makes all the chapters easier for the students with their simple and clean approach towards explaining concepts.

5. For the preparation of exams in the long run, where should I place RS Aggarwal's Solutions to score better marks?

RS Aggarwal is one of the most important contributions in the field of Maths because it makes all the chapters simple and easy for all students alike - the weak, the average, the strong, therefore, the experts also recommend it. Students must follow some rules in the long run. First, the student needs to cover the NCERT chapter then move to RS Aggarwal’s Solutions. RS Aggarwal Class 10 Maths Solutions are designed by specialists and extremely qualified experts who have in-depth information on the updated course of study hence the student goes to the examination hall fully prepared with confidence. RS Aggarwal is a very important and crucial source and it makes Maths easier to understand and approachable for many students.