Chapter 8 of the RD Sharma Class 10 book focuses on this crucial topic, helping students master concepts like solving quadratic equations using different methods—factorization, completing the square, and the quadratic formula. The RD Sharma Class 10 Solutions Chapter 8 are designed to make these concepts simple and clear.
These step-by-step RD Sharma Class 10 Solutions 2025–26 align well with the latest syllabus and exam pattern of NCERT Solutions for Class 10 Maths. Whether you are preparing for board exams or want to build a strong base in algebra, these solutions offer detailed explanations to every question from RD Sharma Class 10 Chapter 8.
Students often find quadratic equations confusing, but with our expertly solved answers in the RD Sharma Quadratic Equations Class 10 Solutions, understanding becomes easier. You can use these materials for revision, practice, and to check your answers.
RD Sharma Class 10 Chapter 8 Quadratic Equations PDF with Solutions
The RD Sharma Class 10 Solutions 2025-26 PDF gives step-wise answers for all exercise questions in Chapter 8. This help you to understand concept better and solve question in exam easily. You can also use the RD Sharma Class 8 Quadratic Equations PDF to practice more problems. These solutions are good for revision and daily practice. If you want to study offline, you can go for RD Sharma Class 8 Quadratic Equations PDF download and use it anytime.
This PDF include solved examples and clear methods. It follow the latest CBSE pattern and useful for school exams. Keep reading to get the free download link and boost your maths preparation.
Important Quadratic Equation Questions of RD Sharma Class 10 - Chapter 8: Quadratic Equations
Q1: Which of the following are quadratic equations?
a) x² + 5x - 6 = 0
b) x³ - 4x = 0
c) 2x² + 7 = 0
Solution:
A quadratic equation has the form ax² + bx + c = 0.
a) Yes, degree is 2.
b) No, degree is 3.
c) Yes, degree is 2.
Q2: Is x = 2 a solution of x² - 3x + 2 = 0?
Solution:
Substitute x = 2:
2² - 3×2 + 2 = 4 - 6 + 2 = 0.
Yes, x = 2 is a solution.
Q3: The product of two consecutive positive integers is 132. Form the quadratic equation if x is the smaller integer.
Solution:
Let integers be x and x+1.
Equation: x(x+1)=132
x² + x - 132 = 0
Q4: Solve x² - 5x + 6 = 0 by factorization.
Solution:
x² - 5x + 6 = 0
(x-2)(x-3) = 0
So x = 2 or x = 3.
Q5: If x² - 8x + 16 = 0, find the sum and product of roots.
Solution:
Sum = -(-8)/1 = 8, Product = 16/1 = 16
Q6: Solve 2x² - 7x + 3 = 0 using quadratic formula.
Solution:
x = [7 ± √(49-24)]/4 = [7 ± 5]/4. So x = 3, x = 0.5
Q7: Solve x² + 4x - 5 = 0 by completing the square.
Solution:
x² + 4x = 5
Add 4: x² + 4x + 4 = 9
(x+2)² = 9 ⇒ x+2 = ±3 ⇒ x = 1, -5
Q8: Find the nature of roots for 3x² + 4x + 2 = 0.
Solution:
D = 4² - 4×3×2 = 16 - 24 = -8 (Negative).
Roots are imaginary.
Q9: For what value of k does x² + kx + 9 = 0 have equal roots?
Solution:
Equal roots if D = 0 ⇒ k² - 36 = 0 ⇒ k = 6, -6
Q10: John and Jivani together have 45 marbles. Both lose 5 marbles each. Their remaining marbles multiply to 128. Find the original marbles if John had x.
Solution:
Jivani had 45-x.
(x-5)(40-x)=128 ⇒ x² - 45x + 328 = 0
Q11: Area of a rectangle is 77 m². Length is 4 more than its breadth. Find its dimensions.
Solution:
Breadth = x, length = x+4.
x(x+4)=77 ⇒ x² + 4x - 77 = 0
Q12: A train covers 480km at a uniform speed. If speed was 8km/h less, it would take 3 hours more. Find the original speed.
Solution:
Let speed be x:
480/(x-8) - 480/x = 3
Q13: For which value of m are roots of x² - 2mx + m² - 1 = 0 real?
Solution:
D = 4m² - 4(m²-1) = 4 (always positive, so real for all m).
Q14: Find roots of x² + 2x + 1 = 0.
Solution:
(x+1)² = 0 ⇒ x = -1 (equal roots)
Q15: Form a quadratic equation whose roots are 3 and -2.
Solution:
Sum = 1, product = -6.
Equation: x² - x - 6 = 0
Q16: Difference of squares of two numbers is 45. Their sum is 13. Find the numbers.
Solution:
Let numbers be x and y.
x + y = 13, x² - y² = 45.
x - y = 45/13. Solve for x and y.
Q17: The area of a rectangle is 528 m². Length is one more than twice its breadth. Find the length and breadth.
Solution:
Breadth = x, Length = 2x+1.
2x² + x - 528 = 0
Q18: Solve for x: 1/x + 1/(x+2) = 1/2
Solution:
2(x+2) + 2x = x(x+2)
4x + 4 = x² + 2x ⇒ x² - 2x - 4 = 0
Q19: Speed of a boat in still water is 8km/hr. It covers 15km upstream and 22km downstream in 5 hours. Find speed of stream.
Solution:
Let stream speed = x.
Upstream: 8-x, Downstream: 8+x.
15/(8-x) + 22/(8+x) = 5. Quadratic to solve.
Q20: In ax² + bx + c = 0. If sum and product of roots are 7 and 12, find the quadratic equation.
Solution:
Sum = 7, product = 12.
Equation: x² - 7x + 12 = 0
RD Sharma Class 10 Solutions Chapter 8 – Quadratic Equations
The RD Sharma Class 10 Solutions Chapter 8 PDF helps students understand quadratic equations in a easy and simple way. This chapter is part of the CBSE Class 10 Maths syllabus 2025-26 and teaches how to solve equations like ax² + bx + c = 0. Many students find this chapter hard, but the RD Sharma Class 10 Quadratic Equations PDF make it simple to learn with clear steps and solved examples.
Main Topics in Chapter 8:
- Meaning of quadratic equation
- Standard form of quadratic equations
- Solving quadratic equations using factorisation method
- Completing the square method
- Quadratic formula method
- Nature of roots and how to find them
- Word problems on quadratic equations
The RD Sharma Class 10 Solutions 2025-26 PDF includes all these topics with solved problems, formulas, and simple tips to help in board exam preparation.
Why Use RD Sharma Class 10 Quadratic Equations PDF?
- Every sums is solved with simple steps
- Good for homework, class tests and board exam preperation
- Helpful for practice and revision
- Can be studied offline after RD Sharma Quadratic Equations PDF download
- Mistake in solving? No worry, steps help you find where it went wrong
Advantages of Practicing Chapter 8 from RD Sharma:
- Build strong base in algebra for future maths topics
- Help in competitive exams like JEE, NTSE, and more
- Improve speed and accuracy by daily solving
- Learn to solve quadratic word problems with confidence
- Solutions based on latest syllabus and exam pattern