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Quantitative Aptitude · Bank exam practice

Quadratic Equations questions for bank exams

Quadratic equation questions give two equations in x and y. You compare the roots and mark x > y, x < y, x ≥ y, x ≤ y or no relation. Plutomonk has 1,040 Quadratic Equations questions in Prelims and Mains sets of 10, each with a worked solution. They are useful for IBPS PO, SBI PO, IBPS Clerk, SBI Clerk, IBPS RRB and RBI Assistant.

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Quick tip

Use the sign rule. When both roots of an equation are negative, the signs in the equation are all positive. This lets you compare without solving fully.

Quadratic Equations sample questions with answers

These are from the first Prelims and Mains sets. Try each question before you open the solution.

Q1. Solve both equations and find the relation between x and y. I. x² − 21x + 110 = 0 II. y² − 6y − 7 = 0

  1. x > y
  2. x < y
  3. x ≥ y
  4. x ≤ y
  5. x = y or no relation can be established
Show answer and solution

Answer: A. x > y

Roots of I: x = 11 and 10. Roots of II: y = -1 and 7. Comparing every pair gives: x > y.

Q2. Solve both equations and find the relation between x and y. I. x² − 5x − 24 = 0 II. y² + 13y + 40 = 0

  1. x > y
  2. x < y
  3. x ≥ y
  4. x ≤ y
  5. x = y or no relation can be established
Show answer and solution

Answer: A. x > y

Roots of I: x = -3 and 8. Roots of II: y = -8 and -5. Comparing every pair gives: x > y.

Q3. Solve both equations and find the relation between x and y. I. x² − 9x − 36 = 0 II. y² + 15y + 54 = 0

  1. x > y
  2. x < y
  3. x ≥ y
  4. x ≤ y
  5. x = y or no relation can be established
Show answer and solution

Answer: A. x > y

Roots of I: x = 12 and -3. Roots of II: y = -6 and -9. Comparing every pair gives: x > y.

Q4. Solve both equations and find the relation between x and y. I. x² − 16x + 48 = 0 II. y² + y − 12 = 0

  1. x > y
  2. x < y
  3. x ≥ y
  4. x ≤ y
  5. x = y or no relation can be established
Show answer and solution

Answer: A. x > y

Roots of I: x = 4 and 12. Roots of II: y = -4 and 3. Comparing every pair gives: x > y.

Q5. Solve both equations and find the relation between x and y. I. x² − 22x + 121 = 0 II. y² − 11y + 18 = 0

  1. x > y
  2. x < y
  3. x ≥ y
  4. x ≤ y
  5. x = y or no relation can be established
Show answer and solution

Answer: A. x > y

Roots of I: x = 11 and 11. Roots of II: y = 9 and 2. Comparing every pair gives: x > y.

Q6. Solve both equations and find the relation between x and y. I. x² − x − 90 = 0 II. y² − 17y + 70 = 0

  1. x > y
  2. x < y
  3. x ≥ y
  4. x ≤ y
  5. x = y or no relation can be established
Show answer and solution

Answer: E. x = y or no relation can be established

Roots of I: x = 10 and -9. Roots of II: y = 7 and 10. Comparing every pair gives: x = y or no relation can be established.

Q7. Solve both equations and find the relation between x and y. I. x² − 9x + 14 = 0 II. y² − 3y + 2 = 0

  1. x > y
  2. x < y
  3. x ≥ y
  4. x ≤ y
  5. x = y or no relation can be established
Show answer and solution

Answer: C. x ≥ y

Roots of I: x = 2 and 7. Roots of II: y = 2 and 1. Comparing every pair gives: x ≥ y.

Q8. Solve both equations and find the relation between x and y. I. x² − 21x + 110 = 0 II. y² − y − 42 = 0

  1. x > y
  2. x < y
  3. x ≥ y
  4. x ≤ y
  5. x = y or no relation can be established
Show answer and solution

Answer: A. x > y

Roots of I: x = 10 and 11. Roots of II: y = 7 and -6. Comparing every pair gives: x > y.

Q9. Solve both equations and find the relation between x and y. I. 3x² + 5x + 2 = 0 II. 10y² + 31y + 24 = 0

  1. x > y
  2. x < y
  3. x ≥ y
  4. x ≤ y
  5. x = y or no relation can be established
Show answer and solution

Answer: A. x > y

Roots of I: x = -2/3 and -1. Roots of II: y = -3/2 and -8/5. Comparing every pair gives: x > y.

Q10. Solve both equations and find the relation between x and y. I. 3x² − 37x + 104 = 0 II. 5y² − y − 18 = 0

  1. x > y
  2. x < y
  3. x ≥ y
  4. x ≤ y
  5. x = y or no relation can be established
Show answer and solution

Answer: A. x > y

Roots of I: x = 13/3 and 8. Roots of II: y = 2 and -9/5. Comparing every pair gives: x > y.

Q11. Solve both equations and find the relation between x and y. I. 12x² + 11x − 5 = 0 II. y² − 7y + 12 = 0

  1. x > y
  2. x < y
  3. x ≥ y
  4. x ≤ y
  5. x = y or no relation can be established
Show answer and solution

Answer: B. x < y

Roots of I: x = -5/4 and 1/3. Roots of II: y = 4 and 3. Comparing every pair gives: x < y.

Q12. Solve both equations and find the relation between x and y. I. 20x² − 73x + 63 = 0 II. 3y² + 8y − 3 = 0

  1. x > y
  2. x < y
  3. x ≥ y
  4. x ≤ y
  5. x = y or no relation can be established
Show answer and solution

Answer: A. x > y

Roots of I: x = 9/4 and 7/5. Roots of II: y = 1/3 and -3. Comparing every pair gives: x > y.

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