RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.5 PDF Download
RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.5 Quadratic Equations has been provided here. Students can refer to these questions before their examinations for better preparation.
Neha Tanna5 Dec, 2024
Share
RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.5: Chapter 8, Exercise 8.5 of RD Sharma Class 10 Maths focuses on solving quadratic equations using the method of factorization. Students are required to factorize the quadratic expression into two binomials and then find the values of .
The exercise covers different types of quadratic equations, including those that require grouping and splitting the middle term. It also reinforces the understanding of roots of the equation and helps in applying factorization techniques to solve real-world problems.RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.5 Overview
Chapter 8, Exercise 8.5 of RD Sharma Class 10 Maths focuses on solving quadratic equations using various methods, including factorization, completing the square, and the quadratic formula. The exercise includes a variety of problems that help students understand the nature of quadratic equations and their solutions. Mastering this exercise is crucial as it forms the foundation for many real-world applications, such as physics, economics, and engineering. Additionally, it helps in developing problem-solving skills and logical thinking, which are essential for higher studies in mathematics and other subjects. The exercise also prepares students for competitive exams and ensures a strong mathematical base.RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.5 PDF
Below, we have provided the RD Sharma Class 10 Maths Chapter 8 Exercise 8.5 Quadratic Equations solutions in PDF format. This exercise covers various methods to solve quadratic equations, including factorization and the quadratic formula. The solutions are detailed and will help students grasp the concepts thoroughly, enabling them to solve similar problems confidently and prepare effectively for exams.RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.5 PDF
RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.5 Quadratic Equations
Below is the RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.5 Quadratic Equations -1. Write the discriminant of the following quadratic equations:
(i) 2x 2 – 5x + 3 = 0
Solution:
Given equation, 2x 2 – 5x + 3 = 0 It is in the form of ax 2 + bx + c = 0 Where, a = 2, b = -5 and c = 3 So, the discriminant is given by D = b 2 – 4ac D = (-5) 2 – 4 x 2 x 3 D = 25 – 24 = 1 Hence, the discriminant of the given quadratic equation is 1.(ii) x 2 + 2x + 4 = 0
Solution:
Given equation, x 2 + 2x + 4 = 0 It is in the form of ax 2 + bx + c = 0 Where, a = 1, b = 2 and c = 4 So, the discriminant is given by D = b 2 – 4ac D = (2) 2 – 4 x 1 x 4 D = 4 – 16 = – 12 Hence, the discriminant of the given quadratic equation is – 12.(iii) (x – 1)(2x – 1) = 0
Solution:
Given equation, (x -1) (2x -1) = 0 On expanding it, we get 2x 2 – 3x + 1 = 0 It is in the form of ax 2 + bx + c = 0 Where, a = 2, b = -3, c = 1 So, the discriminant is given by D = b 2 – 4ac D = (-3) 2 – 4 x 2 x 1 D = 9 – 8 = 1 Hence, the discriminant of the given quadratic equation is 1.(iv) x 2 -2x + k = 0, k ∈ R
Solution:
Given equation, x 2 – 2x + k = 0 It is in the form of ax 2 + bx + c = 0 Where, a = 1, b = -2, and c = k So, the discriminant is given by D = b 2 – 4ac D = (-2) 2 – 4(1)(k) = 4 – 4k Hence, the discriminant of the given equation is (4 – 4k).
(v)
Solution:
(vi) x 2 – x + 1 = 0
Solution:
Given equation, x 2 – x + 1 = 0 It is in the form of ax 2 + bx + c = 0 Where, a = 1, b = -1 and c = 1 So, the discriminant is given by D = b 2 – 4ac D = (-1) 2 – 4 × 1 × 1 D = 1 – 4 = – 3 Thus, the discriminant of the given equation is -3.Benefits of Using RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.5
Using RD Sharma Solutions for Class 10 Maths Chapter 8, Exercise 8.5 (Quadratic Equations) can offer several benefits:1. Step-by-Step Explanations:
RD Sharma solutions provide detailed, step-by-step solutions for each problem in Exercise 8.5. This makes it easier for students to follow the logical progression required to solve quadratic equations, especially for concepts like factorization, completing the square, and using the quadratic formula.2. Clear Conceptual Understanding:
The solutions help students understand the fundamental concepts of quadratic equations, such as: What a quadratic equation is. Methods to solve quadratic equations. The discriminant and its significance. These foundational concepts are explained clearly, reinforcing the knowledge needed for problem-solving.3. Variety of Problems:
Exercise 8.5 offers a variety of problems ranging from basic to more advanced levels. RD Sharma Solutions ensure that all types of problems are covered, helping students practice and master different techniques required to solve quadratic equations.4. Better Time Management:
By using RD Sharma Solutions, students can learn time-saving tricks and techniques for solving quadratic equations more efficiently. This is especially useful when preparing for exams like the CBSE Class 10 Board Exams or entrance tests.5. Quick Revision Tool:
For students who are revising the topic, RD Sharma Solutions act as a quick reference guide. They can quickly check their answers and identify any mistakes they might have made, making it an effective tool for last-minute revisions.6. Boosts Confidence:
With the help of RD Sharma Solutions, students can solve quadratic equations with more confidence. Clear, accurate solutions help to build a deeper understanding, eliminating confusion and boosting overall performance.RD Sharma Solutions Class 10 Maths Chapter 8 Exercise 8.5 FAQs
What are the conditions for a quadratic equation?
A quadratic equation is a second order equation written as ax2+bx+c=0 where a, b, and c are coefficients of real numbers and a≠0.
What are the basic concepts in the quadratic equations?
A quadratic equation can be expressed in the general form of ax2+bx+c=0, where a, b and c are numerical coefficients or constants, and the value of x is variable. One fundamental rule of a quadratic equation is that the value of the first constant never can be zero.
What is the purpose of a quadratic equation?
Quadratic equations are used in many real-life situations such as calculating the areas of an enclosed space, the speed of an object, the profit and loss of a product, or curving a piece of equipment for designing.
What solutions can quadratic equations have?
A quadratic equation whose coefficients are real numbers can have either zero, one, or two distinct real-valued solutions, also called roots.
🔥 Trending Blogs
Talk to a counsellorHave doubts? Our support team will be happy to assist you!
Join 15 Million students on the app today!
Live & recorded classes available at easeDashboard for progress trackingMillions of practice questions at your fingertips
Free Learning Resources
PW Books
Notes (Class 10-12)
PW Study Materials
Notes (Class 6-9)
Ncert Solutions
Govt Exams
Class 6th to 12th Online Courses
Govt Job Exams Courses
UPSC Coaching
Defence Exam Coaching
Gate Exam Coaching
Other Exams
Know about Physics Wallah
Physics Wallah is an Indian edtech platform that provides accessible & comprehensive learning experiences to students from Class 6th to postgraduate level. We also provide extensive NCERT solutions, sample paper, NEET, JEE Mains, BITSAT previous year papers & more such resources to students. Physics Wallah also caters to over 3.5 million registered students and over 78 lakh+ Youtube subscribers with 4.8 rating on its app.
We Stand Out because
We provide students with intensive courses with India’s qualified & experienced faculties & mentors. PW strives to make the learning experience comprehensive and accessible for students of all sections of society. We believe in empowering every single student who couldn't dream of a good career in engineering and medical field earlier.
Our Key Focus Areas
Physics Wallah's main focus is to make the learning experience as economical as possible for all students. With our affordable courses like Lakshya, Udaan and Arjuna and many others, we have been able to provide a platform for lakhs of aspirants. From providing Chemistry, Maths, Physics formula to giving e-books of eminent authors like RD Sharma, RS Aggarwal and Lakhmir Singh, PW focuses on every single student's need for preparation.
What Makes Us Different
Physics Wallah strives to develop a comprehensive pedagogical structure for students, where they get a state-of-the-art learning experience with study material and resources. Apart from catering students preparing for JEE Mains and NEET, PW also provides study material for each state board like Uttar Pradesh, Bihar, and others
Copyright © 2025 Physicswallah Limited All rights reserved.
