The solutions for Chapter 14 – Quadratic Equations from RD Sharma's Class 11 Maths textbook are designed to support students in understanding concepts thoroughly and performing well in exams. In previous classes, you may have studied quadratic equations with real numbers for both coefficients and roots. This chapter takes you a step ahead by introducing complex roots while keeping the coefficients real. It also covers how to solve quadratic equations when both coefficients and roots are complex using the complex number system.
Students can refer to the RD Sharma Class 11 Maths Chapter 14 Solutions provided here to build a solid foundation in these advanced topics. The downloadable PDF links for the solutions are available below for easy access.
RD Sharma Solutions Class 11 Maths Chapter 14 : Overview
Chapter 14 includes two exercises, each containing questions based on the new concepts introduced. The RD Sharma Solutions provide step-by-step answers to all questions, crafted by subject experts to make learning easy and effective.
By solving these problems regularly, students will gain confidence and a deeper understanding of the topic. It is especially helpful for those aiming to score higher in school or board exams.
-
Important definitions and properties related to quadratic equations
-
Quadratic equations with real coefficients
-
Quadratic equations with complex coefficients
RD Sharma Solutions Class 11 Maths Chapter 14 - Quadratic Equations Question with Answers
1. Solve: x² − 5x + 6 = 0
Solution: (x − 2)(x − 3) = 0 ⇒ x = 2, 3
2. Solve: x² + 7x + 12 = 0
Solution: (x + 3)(x + 4) = 0 ⇒ x = −3, −4
3. Solve: x² − 4x + 4 = 0
Solution: (x − 2)² = 0 ⇒ x = 2 (repeated root)
4. Solve: x² + 6x + 10 = 0
Solution: D = 36 − 40 = −4 ⇒ x = −3 ± i
5. Solve: 2x² − 7x + 3 = 0
Solution: D = 25 ⇒ x = (7 ± 5)/4 ⇒ x = 3, 0.5
6. Find the nature of roots: x² − 2x + 5 = 0
Solution: D = −16 ⇒ Imaginary
7. Solve using completing square: x² + 4x + 1 = 0
Solution: (x + 2)² = 3 ⇒ x = −2 ± √3
8. Find k if 2x² + kx + 3 = 0 has equal roots
Solution: k² − 24 = 0 ⇒ k = ±2√6
9. Solve: 3x² = 2x + 1
Solution: 3x² − 2x − 1 = 0 ⇒ x = 1, −1/3
10. Solve: x² − 1 = 0
Solution: x = ±1
11. Solve: x² + 2x + 1 = 0
Solution: x = −1
12. Find k if x² + 2x + k = 0 has real and equal roots
Solution: D = 4 − 4k = 0 ⇒ k = 1
13. If roots are equal, prove b² = 4ac for ax² + bx + c = 0
Solution: Equal roots ⇒ D = 0 ⇒ b² = 4ac
14. Solve: x² + 1 = 0
Solution: x = ±i
15. Solve: 5x² − 20 = 0
Solution: x² = 4 ⇒ x = ±2
16. Solve: x² + 10x + 25 = 0
Solution: (x + 5)² = 0 ⇒ x = −5
17. Solve: 4x² − 4x + 1 = 0
Solution: (2x − 1)² = 0 ⇒ x = ½
18. Solve: x² − 10x + 25 = 0
Solution: (x − 5)² = 0 ⇒ x = 5
19. Solve: x² − 3x − 4 = 0
Solution: (x − 4)(x + 1) ⇒ x = 4, −1
20. Solve: x² − 9 = 0
Solution: x = ±3
21. Find roots of: x² + 2x − 8 = 0
Solution: (x + 4)(x − 2) ⇒ x = −4, 2
22. Solve using formula: x² − 8x + 15 = 0
Solution: x = 5, 3
23. Solve: 2x² + 3x − 2 = 0
Solution: x = 0.5, −2
24. Solve: x² − 6x + 13 = 0
Solution: D = −16 ⇒ x = 3 ± 2i
25. If roots are 2 and 3, find p and q in x² + px + q = 0
Solution: Sum = 5 ⇒ p = −5; Product = 6 ⇒ q = 6
26. Find roots: x² − 2√2x + 2 = 0
Solution: D = 0 ⇒ x = √2
27. Solve: x² + 5x + 6 = 0
Solution: (x + 2)(x + 3) ⇒ x = −2, −3
28. Discriminant of: 3x² + 2x + 1
Solution: D = −8 ⇒ Imaginary roots
29. Solve: 6x² − 5x − 6 = 0
Solution: x = 1.5, −0.67
30. Solve: x² − (a + b)x + ab = 0
Solution: x = a, b
31. If one root is double the other, solve: x² − 5x + 6 = 0
Solution: Roots not in 1:2 ratio ⇒ Not possible
32. If roots of x² + kx + 5 = 0 differ by 1, find k
Solution: Let α, α+1 ⇒ Form quadratic using sum and product, solve for k
Frequently Asked Questions
Chapter 14 introduces students to quadratic equations, their standard form (ax² + bx + c = 0), and different methods to solve them. The chapter covers:
-
Factorization method
-
Completing the square
-
Quadratic formula
-
Discriminant and nature of roots
-
Word problems and real-life applications
This chapter builds a strong algebraic foundation for advanced topics like functions and calculus.
There are seven exercises in Chapter 14, each focusing on a specific technique or concept, such as:
-
Solving quadratic equations
-
Identifying the nature of roots
-
Application-based questions
-
Problems with real and complex solutions
These exercises gradually help students master the topic.
The discriminant D = b² − 4ac determines the nature of roots:
-
D > 0: Real and distinct roots
-
D = 0: Real and equal roots
-
D < 0: Complex (imaginary) roots
Understanding D helps predict the type of solution without solving the equation.
Yes. The RD Sharma Solutions provide a step-by-step approach to each question, which is extremely helpful for JEE, NDA, CUET, and board exams. Practicing these problems improves speed, accuracy, and conceptual clarity in algebra.
You can download exercise-wise PDF solutions for RD Sharma Chapter 14 – Quadratic Equations from educational platforms like Infinity Learn, where expert-created solutions follow the latest CBSE guidelines.