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LIC ADO Quadratic Equations Questions with Answers & Explanations

20 Quadratic Equations questions from the Quantitative Aptitude section of LIC ADO, each with the correct answer and a worked explanation. Try each question first, then tap Show answer to check. When you're ready, take the timed chapter-wise test to see your all-India rank.

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Question 1

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 7x + 10 = 0 II. y² − 15y + 54 = 0

  1. Ax = y or relationship cannot be established
  2. Bx ≤ y
  3. Cx < y
  4. Dx ≥ y
  5. Ex > y
Show answer
Answer: (C) x < y Roots of I: 5, 2. Roots of II: 6, 9. Comparing every pair gives: x < y.
Question 2

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 8x − 9 = 0 II. y² + 6y + 9 = 0

  1. Ax = y or relationship cannot be established
  2. Bx > y
  3. Cx < y
  4. Dx ≤ y
  5. Ex ≥ y
Show answer
Answer: (A) x = y or relationship cannot be established Roots of I: 1, -9. Roots of II: -3, -3. Comparing every pair gives: x = y or relationship cannot be established.
Question 3

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 2x − 8 = 0 II. y² + 15y + 54 = 0

  1. Ax > y
  2. Bx = y or relationship cannot be established
  3. Cx < y
  4. Dx ≤ y
  5. Ex ≥ y
Show answer
Answer: (A) x > y Roots of I: 4, -2. Roots of II: -9, -6. Comparing every pair gives: x > y.
Question 4

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 1x − 6 = 0 II. y² − 3y + 2 = 0

  1. Ax > y
  2. Bx ≤ y
  3. Cx ≥ y
  4. Dx = y or relationship cannot be established
  5. Ex < y
Show answer
Answer: (D) x = y or relationship cannot be established Roots of I: -3, 2. Roots of II: 1, 2. Comparing every pair gives: x = y or relationship cannot be established.
Question 5

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 1x − 6 = 0 II. y² + 4y − 12 = 0

  1. Ax = y or relationship cannot be established
  2. Bx > y
  3. Cx ≥ y
  4. Dx ≤ y
  5. Ex < y
Show answer
Answer: (A) x = y or relationship cannot be established Roots of I: -3, 2. Roots of II: -6, 2. Comparing every pair gives: x = y or relationship cannot be established.
Question 6

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 4x − 45 = 0 II. y² − 64 = 0

  1. Ax ≤ y
  2. Bx = y or relationship cannot be established
  3. Cx > y
  4. Dx < y
  5. Ex ≥ y
Show answer
Answer: (B) x = y or relationship cannot be established Roots of I: 9, -5. Roots of II: -8, 8. Comparing every pair gives: x = y or relationship cannot be established.
Question 7

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 2x − 3 = 0 II. y² + 8y − 9 = 0

  1. Ax > y
  2. Bx ≥ y
  3. Cx < y
  4. Dx = y or relationship cannot be established
  5. Ex ≤ y
Show answer
Answer: (D) x = y or relationship cannot be established Roots of I: 1, -3. Roots of II: -9, 1. Comparing every pair gives: x = y or relationship cannot be established.
Question 8

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 1x − 20 = 0 II. y² + 3y − 28 = 0

  1. Ax < y
  2. Bx ≤ y
  3. Cx = y or relationship cannot be established
  4. Dx ≥ y
  5. Ex > y
Show answer
Answer: (C) x = y or relationship cannot be established Roots of I: 5, -4. Roots of II: -7, 4. Comparing every pair gives: x = y or relationship cannot be established.
Question 9

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 8x + 15 = 0 II. y² − 6y + 8 = 0

  1. Ax > y
  2. Bx = y or relationship cannot be established
  3. Cx ≤ y
  4. Dx < y
  5. Ex ≥ y
Show answer
Answer: (B) x = y or relationship cannot be established Roots of I: 3, 5. Roots of II: 2, 4. Comparing every pair gives: x = y or relationship cannot be established.
Question 10

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 17x + 72 = 0 II. y² + 5y − 14 = 0

  1. Ax > y
  2. Bx ≥ y
  3. Cx ≤ y
  4. Dx = y or relationship cannot be established
  5. Ex < y
Show answer
Answer: (E) x < y Roots of I: -8, -9. Roots of II: -7, 2. Comparing every pair gives: x < y.

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Question 11

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 25 = 0 II. y² + 9y + 18 = 0

  1. Ax ≤ y
  2. Bx < y
  3. Cx = y or relationship cannot be established
  4. Dx ≥ y
  5. Ex > y
Show answer
Answer: (C) x = y or relationship cannot be established Roots of I: -5, 5. Roots of II: -3, -6. Comparing every pair gives: x = y or relationship cannot be established.
Question 12

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 3x − 4 = 0 II. y² − 10y + 16 = 0

  1. Ax = y or relationship cannot be established
  2. Bx ≤ y
  3. Cx > y
  4. Dx ≥ y
  5. Ex < y
Show answer
Answer: (A) x = y or relationship cannot be established Roots of I: 4, -1. Roots of II: 8, 2. Comparing every pair gives: x = y or relationship cannot be established.
Question 13

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 81 = 0 II. y² + 4y + 4 = 0

  1. Ax ≤ y
  2. Bx ≥ y
  3. Cx < y
  4. Dx > y
  5. Ex = y or relationship cannot be established
Show answer
Answer: (E) x = y or relationship cannot be established Roots of I: -9, 9. Roots of II: -2, -2. Comparing every pair gives: x = y or relationship cannot be established.
Question 14

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 6x − 27 = 0 II. y² − 1y − 56 = 0

  1. Ax < y
  2. Bx ≥ y
  3. Cx ≤ y
  4. Dx = y or relationship cannot be established
  5. Ex > y
Show answer
Answer: (D) x = y or relationship cannot be established Roots of I: -3, 9. Roots of II: -7, 8. Comparing every pair gives: x = y or relationship cannot be established.
Question 15

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 3x − 10 = 0 II. y² + 6y − 7 = 0

  1. Ax ≥ y
  2. Bx < y
  3. Cx > y
  4. Dx = y or relationship cannot be established
  5. Ex ≤ y
Show answer
Answer: (D) x = y or relationship cannot be established Roots of I: 5, -2. Roots of II: 1, -7. Comparing every pair gives: x = y or relationship cannot be established.
Question 16

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 1x − 2 = 0 II. y² + 5y − 6 = 0

  1. Ax = y or relationship cannot be established
  2. Bx ≤ y
  3. Cx > y
  4. Dx ≥ y
  5. Ex < y
Show answer
Answer: (A) x = y or relationship cannot be established Roots of I: 1, -2. Roots of II: 1, -6. Comparing every pair gives: x = y or relationship cannot be established.
Question 17

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 4x − 32 = 0 II. y² − 4y + 3 = 0

  1. Ax ≤ y
  2. Bx = y or relationship cannot be established
  3. Cx ≥ y
  4. Dx > y
  5. Ex < y
Show answer
Answer: (B) x = y or relationship cannot be established Roots of I: 8, -4. Roots of II: 1, 3. Comparing every pair gives: x = y or relationship cannot be established.
Question 18

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 7x − 18 = 0 II. y² − 9y + 8 = 0

  1. Ax = y or relationship cannot be established
  2. Bx ≥ y
  3. Cx < y
  4. Dx > y
  5. Ex ≤ y
Show answer
Answer: (A) x = y or relationship cannot be established Roots of I: 2, -9. Roots of II: 8, 1. Comparing every pair gives: x = y or relationship cannot be established.
Question 19

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 10x + 24 = 0 II. y² + 5y + 4 = 0

  1. Ax ≤ y
  2. Bx = y or relationship cannot be established
  3. Cx > y
  4. Dx < y
  5. Ex ≥ y
Show answer
Answer: (C) x > y Roots of I: 6, 4. Roots of II: -4, -1. Comparing every pair gives: x > y.
Question 20

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 4 = 0 II. y² + 5y − 14 = 0

  1. Ax > y
  2. Bx ≥ y
  3. Cx ≤ y
  4. Dx = y or relationship cannot be established
  5. Ex < y
Show answer
Answer: (D) x = y or relationship cannot be established Roots of I: -2, 2. Roots of II: -7, 2. Comparing every pair gives: x = y or relationship cannot be established.

These are RankerClub practice questions written in the LIC ADO pattern. They are not official SSC/IBPS/RRB papers.

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