RS Aggarwal Solutions Class 10 Chapter 10 - Quadratic Equations (Ex 10B) Exercise 10.2

Q: 1. What is a Quadratic Equation?

A quadratic equation is an equation in the form ax2+bx+c=0, where a ≠ 0. This equation can be written in factored form as follows: (x-x1)(x-x2)=0where x1 and x2 are roots of the equation, that is, the values of x for which ax2+bx+c=0. This equation has two solutions, x1 and x2. Quadratic equation questions are usually asked in board exams. Students find it difficult to complete the square and solve quadratic equations. After reading these steps, students will be able to complete the square and solve quadratic equations easily.

RS Aggarwal Solutions

RS Aggarwal Solutions Class 10 Chapter 10 - Quadratic Equations (Ex 10B) Exercise 10.2

Last updated date: 25th Apr 2024

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RS Aggarwal Solutions Class 10 Chapter 10 - Quadratic Equations (Ex 10B) Exercise 10.2 - Free PDF

Free PDF download of RS Aggarwal Solutions Class 10 Chapter 10 – Quadratic Equations (Ex 10B) Exercise 10.2 solved by expert Mathematics teachers is available on Vedantu.com. All Ex 10.2 questions with solutions for RS Aggarwal Class 10 Maths help you to revise the complete syllabus and score more marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams on Vedantu Register online for Class 10 Science tuition on Vedantu.com to score more marks in CBSE board examination.

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Class 10 Chapter 10 – Quadratic Equations

The RS Aggarwal book is prepared for students of all boards and classes and helps students in their exam preparation. One important point to note about the RS Aggarwal solutions for Class 10 Maths Chapter 10 – Quadratic Equations is that it has been divided into two parts. The first part tells you the basics of solving a quadratic equation by completing the square, while the second part deals with the quadratic equation in standard form.

What are Quadratic Equations?

Quadratic equations are second-degree polynomials that have the general form:

ax²+bx+c=0. In this equation, a is non-zero and becomes –b/a if b≠0. The two solutions of the quadratic equation, i.e., x₁ and x₂, are the roots of the equation.

Completing the square:

To solve a quadratic equation by completing the square, you need to complete the square of one side of the equation and then use the Quadratic Formula to find its two roots. The steps involved in completing the square are as follows:

Write the quadratic equation in the form (x+k)²=q .
Substitute p and q for x and a, respectively, such that 3x²+2px+q=0 is obtained by completing the square of one side. Also, note that since k is equal to p, it can be written as –p.
The coefficient of 'x' should be positive, i.e., -3 ≤ 2p ≤ 3; since p is negative, the value of 'k' will always be negative too.
Factor out (x + k) from both sides of the equation to obtain (x+k)²=q.
Square (x+k) on both sides of the equation to obtain x²+2kx+k²=q².
Add k²-q² to both sides of the equation, such that x²+2kx+k²-q²=0 is obtained.
Now, factor x²+2kx+k²-q²=0 on both sides of the equation to obtain (x+k) (x + k) = 0.
Move all terms containing 'x' to the left-hand side and all terms containing 'k', including –p and –q to the right-hand side of the equation.

This gives you the final form of the quadratic equation in standard form, i.e.,ax²+bx+c=0, where a, b, and c are constants and x is the only variable.

Standard Quadratic Equation:

The standard form of a quadratic equation is of the form:

ax²+bx+c=0, where a ≠ 0. This quadratic equation can be written in factored form as follows:

(x-x₁)(x-x₂)=0, where x1 and x2 are roots of quadratic equation, i.e., the values of x for which ax²+bx+c=0 or (x-x₁)(x-x₂)=0.

FAQs on RS Aggarwal Solutions Class 10 Chapter 10 - Quadratic Equations (Ex 10B) Exercise 10.2

1. What is a Quadratic Equation?

A quadratic equation is an equation in the form ax²+bx+c=0, where a ≠ 0. This equation can be written in factored form as follows: (x-x₁)(x-x₂)=0where x₁ and x₂ are roots of the equation, that is, the values of x for which ax²+bx+c=0. This equation has two solutions, x₁ and x₂.

Quadratic equation questions are usually asked in board exams. Students find it difficult to complete the square and solve quadratic equations. After reading these steps, students will be able to complete the square and solve quadratic equations easily.

2. How do I solve a quadratic equation?

There are several methods to solving quadratic equations: the quadratic formula, completing the square and factoring. In this article, we will discuss completing the square. To solve a quadratic equation by completing the square, you need to complete the square of one side of the equation and then use the quadratic formula to find its two roots. After completing the square, the coefficient of 'x' should be positive, i.e., –3 ≤ 2p ≤ 3. Students tackling quadratic equations for the first time often make mistakes at this step. The value of 'k' will always be negative too.

3. Is it necessary that a quadratic equation must have two solutions?

No, a quadratic equation need not have two solutions. If the discriminant (b²-4ac) is equal to zero, then there will be two real solutions. If the discriminant is negative, there will be no real solution. If the discriminant is positive but less than 2, there will be exactly one real solution and many complex solutions. If the discriminant is greater than 2, there will be two complex solutions. You can use the quadratic formula to find all the solutions of a quadratic equation, whether they are real or complex.

4. What are the benefits of completing the square?

Completing the square is a very efficient method for solving quadratic equations. It is much faster than using the quadratic formula, and it always produces two real solutions. In addition, it is a very straightforward method to follow and does not require any complex algebraic manipulation. You can complete the square of any quadratic equation, regardless of its form. You should practise completing the square as much as possible. Vedantu helps students learn in a smart way. RS Aggarwal Solutions Class 10 Chapter 10 – Quadratic Equations will help students score more marks in the examination.