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Quadratic equations practice questions for bank exams

By the PrepMatic team · Updated 9 Oct 2026 · 4 min read

A quadratic equation question gives one equation in x and one in y. You solve both and compare every root of x with every root of y. The five answer options are fixed, so you need only the order of the roots, not exact values. Solve the five sets below at about 60 seconds a pair.

How the question works

Each set looks like this: I. x² − 9x + 20 = 0 and II. y² − 11y + 30 = 0. Each equation has two roots, so there are four x–y pairs to compare. The options are always the same five:

Pick E when the roots overlap, with one x above some y and another x below it.

Five practice questions

In each question, solve both equations and choose the relation between x and y.

Question 1

I. x² − 9x + 20 = 0 and II. y² − 11y + 30 = 0

• A. x > y
• B. x ≥ y
• C. x < y
• D. x ≤ y
• E. x = y or no relation

Question 2

I. x² − 5x − 14 = 0 and II. y² − 3y − 4 = 0

• A. x > y
• B. x ≥ y
• C. x < y
• D. x ≤ y
• E. x = y or no relation

Question 3

I. 2x² − 11x + 15 = 0 and II. 2y² − 9y + 10 = 0

• A. x > y
• B. x ≥ y
• C. x < y
• D. x ≤ y
• E. x = y or no relation

Question 4

I. 6x² + 5x − 6 = 0 and II. y² − 3y + 2 = 0

• A. x > y
• B. x ≥ y
• C. x < y
• D. x ≤ y
• E. x = y or no relation

Question 5

I. 2x² − 7x + 6 = 0 and II. y² + 4y + 3 = 0

• A. x > y
• B. x ≥ y
• C. x < y
• D. x ≤ y
• E. x = y or no relation

Answers and explanations

1. D. (x − 4)(x − 5) = 0 gives x = 4 or 5. (y − 5)(y − 6) = 0 gives y = 5 or 6. Every x is at most every y, and x = y = 5 is possible. So x ≤ y.
2. E. (x − 7)(x + 2) = 0 gives x = 7 or −2. (y − 4)(y + 1) = 0 gives y = 4 or −1. The root x = 7 is above both y values, while x = −2 is below y = 4 and also below y = −1. No single relation holds.
3. B. (2x − 5)(x − 3) = 0 gives x = 2.5 or 3. (2y − 5)(y − 2) = 0 gives y = 2.5 or 2. The smallest x (2.5) is equal to or above both y values, and 3 is above both. So x ≥ y.
4. C. (3x − 2)(2x + 3) = 0 gives x = 2/3 or −3/2. (y − 1)(y − 2) = 0 gives y = 1 or 2. Both x values are below both y values. So x < y.
5. A. (2x − 3)(x − 2) = 0 gives x = 1.5 or 2. (y + 1)(y + 3) = 0 gives y = −1 or −3. Both x values are positive and both y values negative. So x > y.

How to prepare quadratic equations

• Factorise by splitting the middle term. For ax² + bx + c, find two numbers whose product is a × c and whose sum is b. For 6x² + 5x − 6, the product is −36 and the pair is 9 and −4, which gives 6x² + 9x − 4x − 6 = 3x(2x + 3) − 2(2x + 3).
• Use signs to save time. If c/a is positive, both roots share a sign, which is the sign of −b/a. If c/a is negative, the roots have opposite signs. Question 5 shows how sign alone can settle the answer: positive roots against negative roots.
• Check with sum and product. The roots add up to −b/a and multiply to c/a. This two-second check catches most slips.
• List roots on a number line. Write both x roots and both y roots in order. If one letter's roots sit entirely on one side, the relation is clear. If they interleave, the answer is E.
• Do not forget the equal sign. Options B and D (≥ and ≤) are the ones students lose marks on, and they need at least one shared root and no crossing.

Some sets need simplifying first, so also revise simplification.

The full quadratic equations topic test is on PrepMatic (about 15 questions, 30 minutes). The Quantitative Aptitude guide places this topic among the others, and the bank exam hub links every exam's pattern.

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