Quadratic equations are a staple of Bank PO Prelims. With 5 questions often packed into under 2 minutes, you cannot afford long division. This guide teaches the fastest quadratic equation shortcut tricks for bank exams: the sign table and the product-sum split for large numbers.
Table of Contents
The Sign Table Trick (Roots from Equation Signs)
For any quadratic equation x² + bx + c = 0, the roots follow this pattern:
| Sign of b | Sign of c | Sign of Roots | Memory Hook |
|---|---|---|---|
| + | + | Both roots negative (−, −) | Same sign, both negative |
| − | + | Both roots positive (+, +) | Same sign, both positive |
| + | − | One positive, one negative; bigger negative | Opposite signs, larger absolute value is negative |
| − | − | One positive, one negative; bigger positive | Opposite signs, larger absolute value is positive |
Product-Sum Split Method
To factor x² + bx + c, find two numbers p and q such that:
- p × q = c (constant term)
- p + q = b (middle coefficient)
Then the roots are simply −p and −q (when signs are standard).
Example 1: x² − 7x + 12 = 0
Need p × q = 12 and p + q = 7. Numbers: 3 and 4.
Roots: 3 and 4.
Example 2: x² + 5x − 24 = 0
Need p × q = −24 and p + q = 5. Numbers: 8 and −3.
Roots: −8 and 3 (because equation sign pattern gives one negative root).
Splitting Large Numbers Instantly
When c is large, list factor pairs of c quickly using divisibility rules:
| Equation | Target Product | Factor Pair | Roots |
|---|---|---|---|
| x² − 23x + 132 = 0 | 132 | 11 × 12 | 11, 12 |
| x² + 19x − 150 = 0 | −150 | 25 × −6 | −25, 6 |
| x² − 37x + 300 = 0 | 300 | 12 × 25 | 12, 25 |
5-Question Practice Quiz
Solve these in under 2 minutes. Compare roots of both equations.
- x² − 9x + 20 = 0 vs y² − 13y + 42 = 0
- x² + 7x − 60 = 0 vs y² − 5y − 84 = 0
- x² − 17x + 72 = 0 vs y² − 19y + 88 = 0
- x² + 11x + 28 = 0 vs y² + 15y + 56 = 0
- x² − 31x + 228 = 0 vs y² − 29y + 210 = 0
Answer Key
| Q | Roots of x | Roots of y | Relation |
|---|---|---|---|
| 1 | 4, 5 | 6, 7 | x < y |
| 2 | −12, 5 | −7, 12 | Cannot be determined |
| 3 | 8, 9 | 8, 11 | x ≤ y |
| 4 | −7, −4 | −8, −7 | x ≥ y |
| 5 | 12, 19 | 14, 15 | Cannot be determined |
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Q1. How many quadratic equation questions come in IBPS PO Prelims?
Usually 5 questions from one set of quadratic comparisons.
Q2. What if the equation is not in standard form?
Divide or multiply to make the coefficient of x² equal to 1 first.
Q3. Can this method be used when a ≠ 1?
Divide the entire equation by a to convert it to standard form, then apply the sign table.
Last updated: June 27, 2026. For Bank PO coaching in Kolkata, call +91-9804490328.