Banking Notes / Quantitative Aptitude / Chapter 3
Chapter 3 of 26

Quadratic Equations

Solve two equations and compare their roots — the exact format banks use to test algebra speed under Quantity I vs Quantity II.

📖 ~10 min read 🏦 Banking Quantitative Aptitude

Introduction

Bank exams give you two equations — one in x, one in y — and ask you to compare their roots. You don't need to solve for a single numeric answer; you need to find all possible values of x and y and compare them using a fixed set of five answer choices.

Standard Answer Choices

OptionMeaning
x > yEvery value of x is greater than every value of y
x ≥ yx is greater than or equal to y
x < yEvery value of x is less than every value of y
x ≤ yx is less than or equal to y
x = y or relationship cannot be establishedValues are equal, or they overlap/cannot be compared

Fast Factorisation Method

For ax² + bx + c = 0, find two numbers whose product = a×c and sum = b. Split the middle term using these numbers, then factor by grouping.

Q1. x² − 7x + 12 = 0    Q2. y² − 9y + 20 = 0
Equation 1: Need two numbers with product 12, sum 7 → 3 and 4. So x = 3 or x = 4.
Equation 2: Need two numbers with product 20, sum 9 → 4 and 5. So y = 4 or y = 5.
Comparing: x = {3, 4}, y = {4, 5}. Since values overlap (x can equal y at 4, or y can exceed x) → relationship cannot be established.
Q1. 2x² − 5x + 2 = 0    Q2. 3y² − 8y + 4 = 0
Equation 1: Product = 4, sum = 5 → split as 2x²−4x−x+2=0 → x = 2 or x = 1/2.
Equation 2: Product = 12, sum = 8 → split as 3y²−6y−2y+4=0 → y = 2 or y = 2/3.
x = {1/2, 2}, y = {2/3, 2}. Comparing minimums: 1/2 < 2/3, and both reach 2 at the top → x ≤ y.
⚠️ Key Insight: Never stop after finding just one root of each equation — bank exam quadratics always have two roots, and the answer depends on comparing the full sets, not a single pair.
💡 Exam Tip: Practice recognising perfect-square-friendly number pairs (products up to ~60) so you can split the middle term mentally within 10 seconds instead of using the discriminant formula.
✅ Practice Focus: Middle-term splitting · Reading the 5 standard comparison options correctly · Handling equations with fractional or negative roots.

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