RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.1 Quadratic Equations

RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.1: Chapter 8 of RD Sharma's Class 10 Maths focuses on Quadratic Equations, a fundamental topic in algebra. Exercise 8.1 introduces the basic concepts of quadratic equations, including their standard form.

RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.1 Overview

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RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.1 PDF

RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.1 PDF

RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.1 Quadratic Equations

1. Which of the following are quadratic equations?

(i) x ² + 6x – 4 = 0

Solution:

(ii) √3x ² – 2x + 1/2 = 0

Solution:

(iii) x ² + 1/x ² = 5

Solution:

(iv) x – 3/x = x ²

Solution:

(v) 2x ² – √(3x) + 9 = 0

Solution:

(vi) x ² – 2x – √x – 5 = 0

Solution:

(vii) 3x ² – 5x + 9 = x ² – 7x + 3

Solution:

(viii) x + 1/x = 1

Solution:

(ix) x ² – 3x = 0

Solution:

(x) (x + 1/x) ² = 3(x + 1/x) + 4

Solution:

(xi) (2x + 1)(3x + 2) = 6(x – 1)(x – 2)

Solution:

(xii) x + 1/x = x ² , x ≠ 0

Solution:

(xiii) 16x ² – 3 = (2x + 5)(5x – 3)

Solution:

(xiv) (x + 2) ³ = x ³ – 4

Solution:

(xv) x(x + 1) + 8 = (x + 2)(x – 2)

Solution:

x(x + 1) + 8 = (x + 2)(x – 2)

2. In each of the following, determine whether the given values are solutions of the given equation or not:

(i) x ² – 3x + 2 = 0 , x = 2 , x = – 1

Solution:

(ii)  x ² + x + 1 = 0, x = 0, x = 1

Solution:

(iii) x ² − 3√3x + 6 = 0 , x = √3 and x = −2√3

Solution:

(iv) x + 1/x = 13/6, x = 5/6, x = 4/3

Solution:

(v)  2x ² – x + 9 = x ² + 4x + 3, x = 2, x = 3

Solution:

(vi) x ² – √2x – 4 = 0, x = -√2, x = -2√2

Solution:

(vii) a ² x ² – 3abx + 2b ² = 0, x = a/b, x = b/a

Solution:

Benefits of Solving RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.1

1. Strengthens Conceptual Understanding

• RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.1 focuses on the basics of quadratic equations, such as their standard form and methods to check if a given equation is quadratic.
• Solving problems helps students grasp the fundamental structure and nature of quadratic equations.

2. Improves Problem-Solving Skills

• Regular practice enhances the ability to identify and solve quadratic equations efficiently.
• Exposure to a variety of question types builds analytical and logical thinking.

3. Prepares for Board Exams

• RD Sharma is known for its exhaustive approach, covering concepts aligned with CBSE board patterns.
• Solving Exercise 8.1 prepares students for similar questions in board exams and builds confidence.

4. Builds Strong Foundation for Advanced Topics

• Quadratic equations form the basis for many advanced topics in higher classes, including calculus and coordinate geometry.
• Early mastery of the basics ensures easier understanding of future topics.

5. Enhances Accuracy and Speed

• Practicing multiple questions helps in minimizing errors and increases speed in solving problems, a crucial skill for both exams and competitive tests.

6. Boosts Confidence

• Solving RD Sharma's problems and verifying solutions improves confidence in tackling similar or more complex problems.