Quadratic Equation – Exercise 4.3 Solutions (Step-by-Step Guide)

   Solve the following quadratic equations by factorization:

1. (x − 4)(x + 2) = 0 Watch Solution
2. (2x + 3)(3x − 7) = 0 Watch Solution
3. 3x² − 14x − 5 = 0 Watch Solution
4. 9x² − 3x − 2 = 0 Watch Solution
5. 1/(x − 1) − 1/(x + 5) = 6/7, x ≠ 1, −5 Watch Solution
6. 6x² + 11x + 3 = 0 Watch Solution
7. 5x² − 3x − 2 = 0 Watch Solution
8. 48x² − 13x − 1 = 0 Watch Solution
9. 3x² = −11x − 10 Watch Solution
10. 25x(x + 1) = −4  Watch Solution
11. 16x − 10/x = 27 Watch Solution
12. 1/x − 1/(x − 2) = 3, x ≠ 0, 2 Watch Solution
13. x − 1/x = 3, x ≠ 0 Watch Solution
14. 1/(x + 4) − 1/(x − 7) = 11/30, x ≠ 4, 7 Watch Solution
15. 1/(x − 3) + 2/(x − 2) = 8/x, x ≠ 0, 2, 3 Watch Solution
16. a²x² − 3abx + 2b² = 0 Watch Solution
17. 9x² − 6b²x − (a⁴ − b⁴) = 0 Watch Solution
18. 4x² + 4bx − (a² − b²) = 0 Watch Solution
19. ax² + (4a² − 3b)x − 12ab = 0 Watch Solution
20. 2x² + ax − a² = 0 Watch Solution
21. 16/x − 1 = 15/(x + 1), x ≠ 0, −1 Watch Solution
22. (x + 3)/(x + 2) = (3x − 7)/(2x − 3), x ≠ −2, 3/2 Watch Solution
23. 2x/(x − 4) + (2x − 5)/(x − 3) = 25/3, x ≠ 3, 4 Watch Solution
24. (x + 3)/(x − 2) − (1 − x)/x = 17/4, x ≠ 0, 2 Watch Solution
25. (x − 3)/(x + 3) − (x + 3)/(x − 3) = 48/7, x ≠ 3, −3 Watch Solution
26. 1/(x − 2) + 2/(x − 1) = 6/x, x ≠ 0 Watch Solution
27. (x + 1)/(x − 1) − (x − 1)/(x + 1) = 5/6, x ≠ 1, −1 Watch Solution
28. (x − 1)/(2x + 1) + (2x + 1)/(x − 1) = 5/2, x ≠ −1/2, 1 Watch Solution
29. 4/x − 3 = 5/(2x + 3), x ≠ 0, −3/2 Watch Solution
30. (x − 4)/(x − 5) + (x − 6)/(x − 7) = 10/3, x ≠ 5, 7 Watch Solution
31. (x − 2)/(x − 3) + (x − 4)/(x − 5) = 10/3, x ≠ 3, 5 Watch Solution
32. (5 + x)/(5 − x) − (5 − x)/(5 + x) = 3 3/4, x ≠ 5, −5 Watch Solution
33. 3/(x + 1) − 1/2 = 2/(3x − 1), x ≠ −1, 1/3 Watch Solution
34. 3/(x + 1) + 4/(x − 1) = 29/(4x − 1), x ≠ 1, −1, 1/4 Watch Solution
35. 2/(x + 1) + 3/[2(x − 2)] = 23/(5x), x ≠ 0, −1, 2 Watch Solution
36. x² − (√3 + 1)x + √3 = 0 Watch Solution
37. 3√5x² + 25x − 10√5 = 0 Watch Solution
38. √3x² − 2√2x − 2√3 = 0 Watch Solution
39. 4√3x² + 5x − 2√3 = 0 Watch Solution
40. √2x² − 3x − 2√2 = 0 Watch Solution
41. x² − (√2 + 1)x + √2 = 0 Watch Solution
42. 3x² − 2√6x + 2 = 0 Watch Solution
43. √2x² + 7x + 5√2 = 0 Watch Solution
44. (m/n)x² + (n/m) = 1 − 2x Watch Solution
45. (x − a)/(x − b) + (x − b)/(x − a) = a/b + b/a Watch Solution
46. 1/[(x − 1)(x − 2)] + 1/[(x − 2)(x − 3)] + 1/[(x − 3)(x − 4)] = 1/6 Watch Solution
47. a/(x − b) + b/(x − a) = 2, x ≠ a, b Watch Solution
48. (x + 1)/(x − 1) + (x − 2)/(x + 2) = 4 − (2x + 3)/(x − 2), x ≠ 1, −2, 2 Watch Solution
49. a/(x − a) + b/(x − b) = 2c/(x − c) Watch Solution
50. x² + 2ab = (2a + b)x Watch Solution
51. (a + b)²x² − 4abx − (a − b)² = 0 Watch Solution
52. a(x² + 1) − x(a² + 1) = 0 Watch Solution
53. x² − x − a(a + 1) = 0 Watch Solution
54. x² + (a + 1/a)x + 1 = 0 Watch Solution
55. abx² + (b² − ac)x − bc = 0 Watch Solution
56. a²b²x² + b²x − a²x − 1 = 0 Watch Solution
57. (x − 1)/(x − 2) + (x − 3)/(x − 4) = 3 1/3, x ≠ 2, 4 Watch Solution
58. 1/(2a + b + 2x) = 1/(2a) + 1/b + 1/(2x) Watch Solution
59. 3[(3x − 1)/(2x + 3)] − 2[(2x + 3)/(3x − 1)] = 5, x ≠ 1/3, −3/2 Watch Solution
60. 3[(7x + 1)/(5x − 3)] − 4[(5x − 3)/(7x + 1)] = 11, x ≠ 3/5, −1/7 Watch Solution
61. (x − 5)(x − 6) = 25/(24)² Watch Solution
62. 7x + 3/x = 35 3/5  Watch Solution