R.D. Sharma Solutions Class 10th: Ch 8 Quadratic Equations Exercise 8.3

Chapter 8 Quadratic Equations R.D. Sharma Solutions for Class 10th Math Exercise 8.3

Solve the following quadratic equations by factorization:

1. (x+4)(x+2) = 0

Solution

We have,
(x-4) (x+2) = 0
⇒ either (x-4) = 0 or (x+2) = 0
⇒ x = 4 or x = -2
Thus, x = 4 and x = -2 are two roots of the equation (x-4) (x+2) = 0

2. (2x+3)(3x-7) = 0

Solution

3. 3x² – 14x – 5 = 0

Solution



4. 9x²-3x-2 = 0

Solution



5. 1/(x-1) - 1/(x+5) = 6/7, x≠1, -5

Solution



6. 6x² + 11x + 3 = 0

Solution



7. 5x² – 3x – 2 = 0

Solution



8. 48x² - 13x – 1= 0

Solution



9. 3x² = -11x – 10

Solution



10. 25x(x+1) = -4

Solution



11. 16x - 10/x = 27

Solution



12. 1/x - 1/(x-2) = 3, x ≠ 0, 2

Solution



13. x - 1/x = 3, x ≠ 0

Solution



14. 1/(x+4) - 1/(x-7) = 11/30, x ≠ 4, 7

Solution



15. 1/(x-3) + 2/(x-2) = 8/x, x ≠ 0, 2, 3

Solution



16. a²x²-3abx + 2b² = 0

Solution



17. 9x² – 6b²x - (a⁴ - b⁴) = 0

Solution



18. 4x² +4bx – (a² – b²)

Solution



19. ax² + (4a² – 3b) x – 12ab = 0

Solution



20 . 2x² + ax - a² = 0

Solution



21. 16/x - 1 = 15/(x+1), x≠ 0, -1

Solution



22. (x+3)/(x+2) = (3x-7)/(2x-3), x ≠ 2, 3/2

Solution



23. 2x/(x-4) + (2x-5)/(x-3) = 25/3, x ≠ 3, 4

Solution



24. (x+3)/(x-2) - (1-x)/x = 17/4, x ≠ 0, 2

Solution



25. (x-3)/(x+3) - (x+3)/(x-3) = 48/7, x ≠ 3, x ≠ -3

Solution



26. 1/(x-2) + 2/(x-1) = 6/x, x ≠ 0

Solution



27. (x+1)/(x-1) - (x-1)/(x+1) = 5/6, x ≠ 1, -1

Solution



28. (x-1)/(2x+1) + (2x+1)/(x-1) = 5/2, x ≠ -1/2, 1

Solution



29. 4/3 - 3 = 5/(2x+3), x ≠ 0, -3/2

Solution



30. (x-4)/(x-5) + (x-6)/(x-7) = 10/3; x≠5, 7

Solution



31. (x-2)/(x+3) + (x-4)/(x-5) = 10/3; x≠3,5

Solution



32. (5+x)/(5-x) - (5-x)/(5+x) = 3¾; x≠ 5, -5

Solution



33. 3/(x+1) - 1/2 = 2/(3x-1), x≠-1, 1/3

Solution



34. 3/(x+1) + 4/(x-1) = 29/(4x-1), x≠ 1, -1, 1/4

Solution



35. 2/(x+1) + 3/2(x-2) = 23/5x, x≠ 0, -1, 2

Solution



36. x² - (√3 +1) x + √3 = 0

Solution



37. 3√5 x² + 25x - 10 √5 = 0

Solution



38. √(3x²) - 2√2x - 2 √3 = 0

Solution


39. 4√3 x² + 5x - 2 √3 = 0

Solution



40. √2 x² - 3x - 2√2 = 0

Solution



41. x² - (√2 + 1)x + √2 = 0

Solution



42. 3x² - 2√6 x + 2 = 0

Solution



43. x² - 4√2 x + 6 = 0

Solution



44. m/n x² + m/n = 1- 2x

Solution



45. (x-a)/(x-b) + (x-b)/(x-a) = a/b + b/a

Solution



46. 1/(x-1)(x-2) + 1(x-2)(x-3) + 1/(x-3)(x-4) = 1/6

Solution



47. a/(x-b) - b/(x-a) = 2, x ≠ a,b

Solution



48. (x+1)/(x-1) + (x-2)/(x+2) = 4 - (2x+3)/(x-2); x≠ 1,-2, 2

Solution



49. a(x-a) + b/(x-b) = 2c/(x-c)

Solution



50. x² + 2ab = (2a+b)x

Solution



51. (a+b)x² - 4abx - (a-b)² = 0

Solution



52. a(x²+1) - x(a²+1) = 0

Solution



53. x² - x - a(a+1) = 0

Solution



54. x² + (a+1/a)x + 1 = 0

Solution



55. abx² + (b²-ac)x - bc = 0

Solution



56. a²b²x²+ b²x - a²x -1 = 0

Solution



57. (x-1)/(x-2) + (x-3)/(x-4) = 3⅓; x≠ 2, 4

Solution



58. 1/(2a+b+2x) = 1/2a + 1/b + 1/2x

Solution



59. 3{(3x-1)/(2x+3) -2{(2x+3)/3x-1)} = 5; x≠ 1/3, -3/2

Solution



60. 3{(7x-1)/(5x-3)} - 4{(5x-3)/(7x+1)} = 11; x≠ 3/5, -1/7

Solution



61. (x-5) (x-6) = 25/(24)²

Solution



63. 7x + 3/x = 35 3/5

Solution