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
Class 11 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.
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Important definitions and properties related to quadratic equations
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Quadratic equations with real coefficients
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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