Algebra solutions quadratic equations solved. Detailed and MCQ

Algebra detailed and MCQ type

🧮 100 Algebra detailed and MCQ type with Answers – Mathematics Practice Quiz

Boost your Algebra skills with these 100 Multiple Choice Questions with detailed Answers. This algebra detailed and MCQ type collection is designed for exam preparation including SSC, Banking, UPSC, IIT-JEE, and school tests. Practicing Algebra MCQs improves problem-solving, speed, and accuracy.

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📘 Algebra MCQs 1–25 (Basics). Don’t worry we will cover 100 Algebra detailed and MCQ type questions and answers in the same page.

  1. If 2x + 3 = 7, then x = ?
    a) 1 ✅
    b) 2
    c) 3
    d) 4
  2. If x² = 16, then x = ?
    a) ±4 ✅
    b) 8
    c) 2
    d) None
  3. Simplify (x + 2)(x + 3).
    a) x² + 5x + 6 ✅
    b) x² + 6x + 5
    c) x² + 2x + 3
    d) None
  4. If x – 5 = 0, then x = ?
    a) 0
    b) 5 ✅
    c) -5
    d) None
  5. If 3x = 12, then x = ?
    a) 2
    b) 3
    c) 4 ✅
    d) 6
  6. If x² – 9 = 0, then x = ?
    a) ±3 ✅
    b) ±9
    c) 0
    d) None
  7. Solve: 5x + 2 = 12.
    a) 1
    b) 2
    c) 3 ✅
    d) 4
  8. If (x + 1)(x – 1) = ?
    a) x² – 1 ✅
    b) x² + 1
    c) x² – x
    d) x² + x
  9. If 10x = 100, then x = ?
    a) 5
    b) 10 ✅
    c) 20
    d) 100
  10. Simplify: (a + b)².
    a) a² + b²
    b) a² + 2ab + b² ✅
    c) 2a² + b²
    d) None
  11. If 4x = 36, then x = ?
    a) 6 ✅
    b) 7
    c) 8
    d) 9
  12. Factorize: x² – 4.
    a) (x – 2)(x + 2) ✅
    b) (x – 4)(x + 1)
    c) (x – 1)(x + 4)
    d) None
  13. If 2x – 5 = 1, then x = ?
    a) 2
    b) 3 ✅
    c) 4
    d) 5
  14. Simplify: (2x + 3)(2x – 3).
    a) 4x² – 9 ✅
    b) 4x² + 9
    c) 2x² – 9
    d) None
  15. If x² = 49, then x = ?
    a) ±7 ✅
    b) 7
    c) -7
    d) None
  16. If x³ = 8, then x = ?
    a) 1
    b) 2 ✅
    c) 3
    d) 4
  17. Solve: 6x – 2 = 10.
    a) 1
    b) 2
    c) 3 ✅
    d) 4
  18. Factorize: x² + 2x + 1.
    a) (x – 1)(x – 1)
    b) (x + 1)(x + 1) ✅
    c) (x + 2)(x + 0.5)
    d) None
  19. Simplify: (x – 2)².
    a) x² + 2x + 4
    b) x² – 4x + 4 ✅
    c) x² – 2
    d) None
  20. If 7x – 14 = 0, then x = ?
    a) 1
    b) 2 ✅
    c) 3
    d) 4
  21. If (x + y)(x – y) = ?
    a) x² – y² ✅
    b) x² + y²
    c) 2xy
    d) None
  22. Solve: 2x + 5 = 15.
    a) 3
    b) 5 ✅
    c) 10
    d) None
  23. Factorize: x² – 5x + 6.
    a) (x – 2)(x – 3) ✅
    b) (x + 2)(x – 3)
    c) (x – 6)(x + 1)
    d) None
  24. Simplify: (a – b)².
    a) a² – b²
    b) a² – 2ab + b² ✅
    c) a² + b² – ab
    d) None
  25. If 3x + 9 = 0, then x = ?
    a) -3 ✅
    b) 3
    c) 0
    d) None

26-50 Algebra detailed and MCQ type

Part 2 – Algebraic Identities & Simplification (26–50) – Step by Step. After completing these Algebra detailed and MCQ type questions your concepts on this topic Will be much more clear.

Q26. Expand (a + b)².
Step by Step:

  1. Use formula: (a + b)² = a² + 2ab + b²
    ✅ Answer: a² + 2ab + b²

Q27. Expand (x – y)².
Step by Step:

  1. Formula: (x – y)² = x² – 2xy + y²
    ✅ Answer: x² – 2xy + y²

Q28. Expand (x + y)(x – y).
Step by Step:

  1. Apply difference of squares: (x + y)(x – y) = x² – y²
    ✅ Answer: x² – y²

Q29. Factorize x² – 9.
Step by Step:

  1. Recognize as difference of squares: x² – 3²
  2. Factor: (x – 3)(x + 3)
    ✅ Answer: (x – 3)(x + 3)

Q30. Factorize x² + 2x + 1.
Step by Step:

  1. Recognize perfect square trinomial: x² + 2x + 1 = (x + 1)²
    ✅ Answer: (x + 1)(x + 1)

Q31. Simplify (2x + 3)(2x – 3).
Step by Step:

  1. Use formula (a + b)(a – b) = a² – b²
  2. Here, a = 2x, b = 3 → (2x)² – 3² = 4x² – 9
    ✅ Answer: 4x² – 9

Q32. Simplify (x + 5)² – (x – 5)².
Step by Step:

  1. Expand both squares: (x + 5)² = x² + 10x + 25, (x – 5)² = x² – 10x + 25
  2. Subtract: (x² + 10x + 25) – (x² – 10x + 25) = 20x
    ✅ Answer: 20x

Q33. Factorize x² – 16.
Step by Step:

  1. Recognize difference of squares: x² – 4²
  2. Factor: (x – 4)(x + 4)
    ✅ Answer: (x – 4)(x + 4)

Q34. Expand (x + 2)(x + 3).
Step by Step:

  1. Apply distributive property: x(x + 3) + 2(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6
    ✅ Answer: x² + 5x + 6

Q35. Expand (3x + 1)(3x – 1).
Step by Step:

  1. Difference of squares: (3x)² – 1² = 9x² – 1
    ✅ Answer: 9x² – 1

Q36. Factorize x² – 6x + 9.
Step by Step:

  1. Recognize perfect square trinomial: x² – 6x + 9 = (x – 3)²
    ✅ Answer: (x – 3)(x – 3)

Q37. Simplify (a + b)³.
Step by Step:

  1. Formula: (a + b)³ = a³ + 3a²b + 3ab² + b³
    ✅ Answer: a³ + 3a²b + 3ab² + b³

Q38. Simplify (x – y)³.
Step by Step:

  1. Formula: (x – y)³ = x³ – 3x²y + 3xy² – y³
    ✅ Answer: x³ – 3x²y + 3xy² – y³

Q39. If x² + 5x + 6 = 0, find factors.
Step by Step:

  1. Factor: Find two numbers multiplying to 6 and adding to 5 → 2 and 3
  2. Factorized: (x + 2)(x + 3) = 0
    ✅ Answer: (x + 2)(x + 3)

Q40. Solve 2x + 3 = 11.
Step by Step:

  1. Subtract 3: 2x = 8
  2. Divide by 2: x = 4
    ✅ Answer: x = 4

Q41. Solve 3x – 5 = 7.
Step by Step:

  1. Add 5: 3x = 12
  2. Divide by 3: x = 4
    ✅ Answer: x = 4

Q42. Factorize x² – x – 6.
Step by Step:

  1. Find two numbers multiplying to -6 and adding to -1 → -3 and 2
  2. Factor: (x – 3)(x + 2)
    ✅ Answer: (x – 3)(x + 2)

Q43. Solve 4x – 7 = 5.
Step by Step:

  1. Add 7: 4x = 12
  2. Divide by 4: x = 3
    ✅ Answer: x = 3

Q44. Factorize x² + 7x + 10.
Step by Step:

  1. Find two numbers multiplying to 10 and adding to 7 → 5 and 2
  2. Factor: (x + 5)(x + 2)
    ✅ Answer: (x + 5)(x + 2)

Q45. Simplify (x + 1)² – (x – 1)².
Step by Step:

  1. Expand: x² + 2x + 1 – (x² – 2x + 1) = 4x
    ✅ Answer: 4x

Q46. Expand (x + 2)(x – 5).
Step by Step:

  1. Multiply: x² – 5x + 2x – 10 = x² – 3x – 10
    ✅ Answer: x² – 3x – 10

Q47. Factorize x² – 2x – 15.
Step by Step:

  1. Find numbers multiplying to -15 and adding to -2 → -5 and 3
  2. Factor: (x – 5)(x + 3)
    ✅ Answer: (x – 5)(x + 3)

Q48. Solve 5x + 2 = 12.
Step by Step:

  1. Subtract 2: 5x = 10
  2. Divide by 5: x = 2
    ✅ Answer: x = 2

Q49. Simplify (2x + 3)².
Step by Step:

  1. Formula: (a + b)² = a² + 2ab + b²
  2. a = 2x, b = 3 → (2x)² + 2(2x3) + 3² = 4x² + 12x + 9
    ✅ Answer: 4x² + 12x + 9

Q50. Simplify (3x – 2)².
Step by Step:

  1. Formula: (a – b)² = a² – 2ab + b²
  2. a = 3x, b = 2 → (3x)² – 2(3x2) + 2² = 9x² – 12x + 4
    ✅ Answer: 9x² – 12x + 4

🔹 What is a Quadratic Equation?

A quadratic equation is a type of algebraic equation of the form:

ax^2 + bx + c = 0

where:

is the variable,

are constants with .

Quadratic equations can have two real roots, one repeated root, or complex roots depending on the discriminant . They are fundamental in algebra and are used in physics, engineering, economics, and many real-life applications.

🔥 Section 3 – Quadratic Equations: MCQs 51–75

These questions focus on quadratic equations, roots, factorization, and discriminant analysis.

Q51. Solve x² – 5x + 6 = 0
Step by Step:

  1. Factorize: Find two numbers multiplying to 6 and adding to –5 → –2 and –3
  2. Factor: (x – 2)(x – 3) = 0
  3. Solve: x – 2 = 0 → x = 2, x – 3 = 0 → x = 3
    ✅ Answer: x = 2 or 3

Q52. Solve x² + 4x + 4 = 0
Step by Step:

  1. Recognize perfect square: x² + 4x + 4 = (x + 2)²
  2. Solve: x + 2 = 0 → x = –2
    ✅ Answer: x = –2 (double root)

Q53. Find α + β if roots of x² – 7x + 10 = 0 are α and β
Step by Step:

  1. Sum of roots formula: α + β = –b/a
  2. Here, a = 1, b = –7 → α + β = 7
    ✅ Answer: 7

Q54. Find α × β if roots of x² – 7x + 10 = 0 are α and β
Step by Step:

  1. Product of roots formula: α × β = c/a
  2. Here, c = 10, a = 1 → α × β = 10
    ✅ Answer: 10

Q55. Solve 2x² – 8x = 0
Step by Step:

  1. Factor: 2x(x – 4) = 0
  2. Solve: x = 0 or x = 4
    ✅ Answer: x = 0 or 4

Q56. Solve x² + 6x + 9 = 0
Step by Step:

  1. Perfect square: (x + 3)² = 0
  2. Solve: x = –3
    ✅ Answer: x = –3 (double root)

Q57. Solve x² – 9x + 20 = 0
Step by Step:

  1. Factor: Numbers multiplying to 20 and adding to –9 → –4 and –5
  2. Factor: (x – 4)(x – 5) = 0
  3. Solve: x = 4 or 5
    ✅ Answer: x = 4 or 5

Q58. Solve 3x² – 12x = 0
Step by Step:

  1. Factor: 3x(x – 4) = 0
  2. Solve: x = 0 or x = 4
    ✅ Answer: x = 0 or 4

Q59. Solve x² – 4x – 5 = 0
Step by Step:

  1. Factor: Numbers multiplying to –5 and adding to –4 → –5 and 1
  2. Factor: (x – 5)(x + 1) = 0
  3. Solve: x = 5 or –1
    ✅ Answer: x = 5 or –1

Q60. Solve x² + 7x + 10 = 0
Step by Step:

  1. Factor: Numbers multiplying to 10 and adding to 7 → 5 and 2
  2. Factor: (x + 5)(x + 2) = 0
  3. Solve: x = –5 or –2
    ✅ Answer: x = –5 or –2

Q61. Solve 2x² – 10x + 12 = 0
Step by Step:

  1. Divide entire equation by 2 → x² – 5x + 6 = 0
  2. Factorize: Find numbers multiplying to 6 and adding to –5 → –2 and –3
  3. Factor: (x – 2)(x – 3) = 0
  4. Solve: x = 2 or x = 3
    ✅ Answer: x = 2 or 3

Q62. Solve x² – x – 12 = 0
Step by Step:

  1. Factorize: Numbers multiplying to –12 and adding to –1 → –4 and 3
  2. Factor: (x – 4)(x + 3) = 0
  3. Solve: x = 4 or x = –3
    ✅ Answer: x = 4 or –3

Q63. Solve 4x² – 25 = 0
Step by Step:

  1. Recognize difference of squares: (2x)² – 5² = 0
  2. Factor: (2x – 5)(2x + 5) = 0
  3. Solve: x = 5/2 or x = –5/2
    ✅ Answer: x = 5/2 or –5/2

Q64. Solve x² + 10x + 25 = 0
Step by Step:

  1. Perfect square trinomial: x² + 10x + 25 = (x + 5)²
  2. Solve: x + 5 = 0 → x = –5
    ✅ Answer: x = –5 (double root)

Q65. Solve x² – 6x + 8 = 0
Step by Step:

  1. Factorize: Numbers multiplying to 8 and adding to –6 → –4 and –2
  2. Factor: (x – 4)(x – 2) = 0
  3. Solve: x = 4 or x = 2
    ✅ Answer: x = 2 or 4

Q66. Solve x² – 3x – 10 = 0
Step by Step:

  1. Factorize: Numbers multiplying to –10 and adding to –3 → –5 and 2
  2. Factor: (x – 5)(x + 2) = 0
  3. Solve: x = 5 or x = –2
    ✅ Answer: x = 5 or –2

Q67. Solve 3x² – 15x + 12 = 0
Step by Step:

  1. Divide by 3: x² – 5x + 4 = 0
  2. Factorize: Numbers multiplying to 4 and adding to –5 → –1 and –4
  3. Factor: (x – 1)(x – 4) = 0
  4. Solve: x = 1 or x = 4
    ✅ Answer: x = 1 or 4

Q68. Solve x² – 8x + 16 = 0
Step by Step:

  1. Recognize perfect square: x² – 8x + 16 = (x – 4)²
  2. Solve: x – 4 = 0 → x = 4
    ✅ Answer: x = 4 (double root)

Q69. Solve 2x² + 7x + 3 = 0
Step by Step:

  1. Multiply ac = 23 = 6 → Find numbers adding to 7 → 6 and 1
  2. Split middle term: 2x² + 6x + x + 3 = 0
  3. Factor: 2x(x + 3) + 1(x + 3) = 0
  4. Factor: (2x + 1)(x + 3) = 0
  5. Solve: x = –1/2 or x = –3
    ✅ Answer: x = –1/2 or –3

Q70. Solve x² + 9x + 14 = 0
Step by Step:

  1. Factor: Numbers multiplying to 14 and adding to 9 → 7 and 2
  2. Factor: (x + 7)(x + 2) = 0
  3. Solve: x = –7 or x = –2
    ✅ Answer: x = –7 or –2

Q71. Solve x² – 10x + 21 = 0
Step by Step:

  1. Factor: Numbers multiplying to 21 and adding to –10 → –3 and –7
  2. Factor: (x – 3)(x – 7) = 0
  3. Solve: x = 3 or x = 7
    ✅ Answer: x = 3 or 7

Q72. Solve 2x² – x – 6 = 0
Step by Step:

  1. Multiply ac = 2(-6) = –12 → Numbers adding to –1 → –4 and 3
  2. Split middle term: 2x² – 4x + 3x – 6 = 0
  3. Factor: 2x(x – 2) + 3(x – 2) = 0
  4. Factor: (2x + 3)(x – 2) = 0
  5. Solve: x = –3/2 or x = 2
    ✅ Answer: x = –3/2 or 2

Q73. Solve x² + 5x + 6 = 0
Step by Step:

  1. Factor: Numbers multiplying to 6 and adding to 5 → 2 and 3
  2. Factor: (x + 2)(x + 3) = 0
  3. Solve: x = –2 or x = –3
    ✅ Answer: x = –2 or –3

Q74. Solve x² – 4x – 21 = 0
Step by Step:

  1. Factor: Numbers multiplying to –21 and adding to –4 → –7 and 3
  2. Factor: (x – 7)(x + 3) = 0
  3. Solve: x = 7 or x = –3
    ✅ Answer: x = 7 or –3

Q75. Solve 3x² + 11x + 6 = 0
Step by Step:

  1. Multiply ac = 36 = 18 → Numbers adding to 11 → 9 and 2
  2. Split middle term: 3x² + 9x + 2x + 6 = 0
  3. Factor: 3x(x + 3) + 2(x + 3) = 0
  4. Factor: (3x + 2)(x + 3) = 0
  5. Solve: x = –2/3 or x = –3
    ✅ Answer: x = –2/3 or –3

🔹 Quadratic Equations & Advanced Algebra: MCQs 76–100

These MCQs cover quadratic equations, higher-order factorization, and application-based algebra problems.

Q76. Solve x² – 2x – 15 = 0
Step by Step:

  1. Factor: Numbers multiplying to –15 and adding to –2 → –5 and 3
  2. Factor: (x – 5)(x + 3) = 0
  3. Solve: x = 5 or –3
    ✅ Answer: x = 5 or –3

Q77. Solve 5x² + 6x – 8 = 0
Step by Step:

  1. Multiply a*c = 5 * –8 = –40 → Numbers adding to 6 → 10 and –4
  2. Split middle term: 5x² + 10x – 4x – 8 = 0
  3. Factor: 5x(x + 2) – 4(x + 2) = 0
  4. Factor: (5x – 4)(x + 2) = 0
  5. Solve: x = 4/5 or –2
    ✅ Answer: x = 4/5 or –2

Q78. Solve x² + x – 20 = 0
Step by Step:

  1. Factor: Numbers multiplying to –20 and adding to 1 → 5 and –4
  2. Factor: (x + 5)(x – 4) = 0
  3. Solve: x = –5 or 4
    ✅ Answer: x = –5 or 4

Q79. Solve 2x² – 7x + 3 = 0
Step by Step:

  1. Multiply ac = 23 = 6 → Numbers adding to –7 → –6 and –1
  2. Split middle term: 2x² – 6x – x + 3 = 0
  3. Factor: 2x(x – 3) – 1(x – 3) = 0
  4. Factor: (2x – 1)(x – 3) = 0
  5. Solve: x = 1/2 or 3
    ✅ Answer: x = 1/2 or 3

Q80. Solve x² – 12x + 36 = 0
Step by Step:

  1. Recognize perfect square: x² – 12x + 36 = (x – 6)²
  2. Solve: x – 6 = 0 → x = 6
    ✅ Answer: x = 6 (double root)

Q81. Solve 3x² – 2x – 8 = 0
Step by Step:

  1. Multiply ac = 3–8 = –24 → Numbers adding to –2 → –6 and 4
  2. Split middle term: 3x² – 6x + 4x – 8 = 0
  3. Factor: 3x(x – 2) + 4(x – 2) = 0
  4. Factor: (3x + 4)(x – 2) = 0
  5. Solve: x = –4/3 or 2
    ✅ Answer: x = –4/3 or 2

Q82. Solve x² + 8x + 15 = 0
Step by Step:

  1. Factor: Numbers multiplying to 15 and adding to 8 → 5 and 3
  2. Factor: (x + 5)(x + 3) = 0
  3. Solve: x = –5 or –3
    ✅ Answer: x = –5 or –3

Q83. Solve 2x² + x – 3 = 0
Step by Step:

  1. Multiply ac = 2–3 = –6 → Numbers adding to 1 → 3 and –2
  2. Split middle term: 2x² + 3x – 2x – 3 = 0
  3. Factor: x(2x + 3) –1(2x + 3) = 0
  4. Factor: (2x + 3)(x – 1) = 0
  5. Solve: x = –3/2 or 1
    ✅ Answer: x = –3/2 or 1

Q84. Solve x² – 11x + 28 = 0
Step by Step:

  1. Factor: Numbers multiplying to 28 and adding to –11 → –7 and –4
  2. Factor: (x – 7)(x – 4) = 0
  3. Solve: x = 7 or 4
    ✅ Answer: x = 4 or 7

Q85. Solve x² + 6x + 5 = 0
Step by Step:

  1. Factor: Numbers multiplying to 5 and adding to 6 → 1 and 5
  2. Factor: (x + 1)(x + 5) = 0
  3. Solve: x = –1 or –5
    ✅ Answer: x = –1 or –5

Q86. Solve 2x² – 5x + 2 = 0
Step by Step:

  1. Multiply ac = 22 = 4 → Numbers adding to –5 → –4 and –1
  2. Split middle term: 2x² – 4x – x + 2 = 0
  3. Factor: 2x(x – 2) –1(x – 2) = 0
  4. Factor: (2x – 1)(x – 2) = 0
  5. Solve: x = 1/2 or 2
    ✅ Answer: x = 1/2 or 2

Q87. Solve x² – 9x + 18 = 0
Step by Step:

  1. Factor: Numbers multiplying to 18 and adding to –9 → –6 and –3
  2. Factor: (x – 6)(x – 3) = 0
  3. Solve: x = 6 or 3
    ✅ Answer: x = 3 or 6

Q88. Solve 3x² + 2x – 8 = 0
Step by Step:

  1. Multiply ac = 3–8 = –24 → Numbers adding to 2 → 6 and –4
  2. Split middle term: 3x² + 6x – 4x – 8 = 0
  3. Factor: 3x(x + 2) –4(x + 2) = 0
  4. Factor: (3x – 4)(x + 2) = 0
  5. Solve: x = 4/3 or –2
    ✅ Answer: x = 4/3 or –2

Q89. Solve x² + 7x + 12 = 0
Step by Step:

  1. Factor: Numbers multiplying to 12 and adding to 7 → 3 and 4
  2. Factor: (x + 3)(x + 4) = 0
  3. Solve: x = –3 or –4
    ✅ Answer: x = –3 or –4

Q90. Solve 2x² – 9x + 7 = 0
Step by Step:

  1. Multiply ac = 27 = 14 → Numbers adding to –9 → –7 and –2
  2. Split middle term: 2x² – 7x – 2x + 7 = 0
  3. Factor: x(2x – 7) –1(2x – 7) = 0
  4. Factor: (2x – 7)(x – 1) = 0
  5. Solve: x = 7/2 or 1
    ✅ Answer: x = 7/2 or 1

Q91. Solve x² – 10x + 24 = 0
Step by Step:

  1. Factor: Numbers multiplying to 24 and adding to –10 → –6 and –4
  2. Factor: (x – 6)(x – 4) = 0
  3. Solve: x = 6 or 4
    ✅ Answer: x = 4 or 6

Q92. Solve x² + 8x + 12 = 0
Step by Step:

  1. Factor: Numbers multiplying to 12 and adding to 8 → 6 and 2
  2. Factor: (x + 6)(x + 2) = 0
  3. Solve: x = –6 or –2
    ✅ Answer: x = –6 or –2

Q93. Solve 3x² – 14x + 8 = 0
Step by Step:

  1. Multiply ac = 38 = 24 → Numbers adding to –14 → –12 and –2
  2. Split middle term: 3x² – 12x – 2x + 8 = 0
  3. Factor: 3x(x – 4) –2(x – 4) = 0
  4. Factor: (3x – 2)(x – 4) = 0
  5. Solve: x = 2/3 or 4
    ✅ Answer: x = 2/3 or 4

Q94. Solve x² – x – 6 = 0
Step by Step:

  1. Factor: Numbers multiplying to –6 and adding to –1 → –3 and 2
  2. Factor: (x – 3)(x + 2) = 0
  3. Solve: x = 3 or –2
    ✅ Answer: x = 3 or –2

Q95. Solve 2x² + 5x + 2 = 0
Step by Step:

  1. Multiply ac = 22 = 4 → Numbers adding to 5 → 4 and 1
  2. Split middle term: 2x² + 4x + x + 2 = 0
  3. Factor: 2x(x + 2) +1(x + 2) = 0
  4. Factor: (2x + 1)(x + 2) = 0
  5. Solve: x = –1/2 or –2
    ✅ Answer: x = –1/2 or –2

Q96. Solve x² – 7x + 12 = 0
Step by Step:

  1. Factor: Numbers multiplying to 12 and adding to –7 → –3 and –4
  2. Factor: (x – 3)(x – 4) = 0
  3. Solve: x = 3 or 4
    ✅ Answer: x = 3 or 4

Q97. Solve 3x² – 11x + 6 = 0
Step by Step:

  1. Multiply ac = 36 = 18 → Numbers adding to –11 → –9 and –2
  2. Split middle term: 3x² – 9x – 2x + 6 = 0
  3. Factor: 3x(x – 3) – 2(x – 3) = 0
  4. Factor: (3x – 2)(x – 3) = 0
  5. Solve: x = 2/3 or x = 3
    ✅ Answer: x = 2/3 or 3

Q98. Solve x² + 4x – 21 = 0
Step by Step:

  1. Factor: Numbers multiplying to –21 and adding to 4 → 7 and –3
  2. Factor: (x + 7)(x – 3) = 0
  3. Solve: x = –7 or x = 3
    ✅ Answer: x = –7 or 3

Q99. Solve 2x² – 3x – 5 = 0
Step by Step:

  1. Multiply ac = 2–5 = –10 → Numbers adding to –3 → 2 and –5
  2. Split middle term: 2x² + 2x – 5x – 5 = 0
  3. Factor: 2x(x + 1) –5(x + 1) = 0
  4. Factor: (2x – 5)(x + 1) = 0
  5. Solve: x = 5/2 or x = –1
    ✅ Answer: x = 5/2 or –1

Q100. Solve x² – 13x + 40 = 0
Step by Step:

  1. Factor: Numbers multiplying to 40 and adding to –13 → –5 and –8
  2. Factor: (x – 5)(x – 8) = 0
  3. Solve: x = 5 or x = 8
    ✅ Answer: x = 5 or 8

✅ Quick Algebra Tips for MCQs:

  1. Learn to Factor Fast

Factorization is the fastest way to solve quadratic equations.

Example: x² – 5x + 6 → (x – 2)(x – 3)

  1. Memorize Common Algebraic Identities

(a + b)² = a² + 2ab + b²

(a – b)² = a² – 2ab + b²

a² – b² = (a – b)(a + b)

  1. Use Sum and Product of Roots Formulas

For ax² + bx + c = 0:

Sum of roots α + β = –b/a

Product of roots α × β = c/a

  1. Skip Difficult Questions First

Solve easy MCQs first, then return to tougher ones.

Saves time and reduces mistakes.

  1. Practice Step-by-Step Solutions

Always write each step clearly; this builds accuracy and confidence.

Frequently Asked Questions (FAQs) on 100 Algebra detailed and MCQ type questions with answers

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Q1: What is a quadratic equation?
A: A quadratic equation is an equation of the form ax² + bx + c = 0 where a ≠ 0. It can have two real roots, one repeated root, or complex roots, depending on the discriminant D = b² – 4ac. Quadratic equations are used in physics, economics, engineering, and math problem solving.

Q2: How can I solve algebra MCQs faster?
A: Use factorization, formula methods, and algebraic shortcuts. Practicing step-by-step solutions improves both speed and accuracy, especially in exams like SSC, Banking, and IIT-JEE.

Q3: Are these Algebra MCQs useful for competitive exams?
A: Yes! Practicing 100 Algebra detailed and MCQ type questions with answers helps you master quadratic equations, linear equations, and algebraic identities, preparing you for SSC, Banking, IIT-JEE, UPSC, and school-level math tests.

Q4: Where can I practice more Algebra MCQs online?
A: You can explore More Algebra detailed and MCQ type solutions and other math quizzes to test your skills and improve problem-solving speed.

Practicing these 100 Algebra detailed and MCQ type questions with step-by-step solutions will strengthen your foundation and improve your exam performance. Don’t stop here—explore more math quizzes to keep challenging yourself and become a math pro!

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