IBPS PO & SBI Clerk Speed Math: Quadratic Equations Sign Table & Factor Tricks
Category: Banking | Subject: Quantitative Aptitude | Topic: Quadratic Equations | Read Time: 4 min
Solve 5 inequality comparison questions in under 90 seconds using the 4-row sign table and split-root shortcuts.
Key Formulas & 10-Second Reference Table
| Concept / Case | Formula / Rule | When to Use |
|---|---|---|
| Equation Form: ax² + bx + c = 0 (+, +) | Root Signs: (−, −) | Both b and c are positive; both roots are negative. |
| Equation Form: ax² − bx + c = 0 (−, +) | Root Signs: (+, +) | Middle term is negative and constant is positive; both roots are positive. |
| Equation Form: ax² + bx − c = 0 (+, −) | Root Signs: (−, +) [Larger magnitude root is negative] | Constant term is negative and b is positive. |
| Equation Form: ax² − bx − c = 0 (−, −) | Root Signs: (+, −) [Larger magnitude root is positive] | Both b and c are negative. |
Instant CND (Cannot Be Determined) Elimination Rule
Before factoring any numbers in IBPS PO or SBI Clerk Prelims, inspect the signs of the constant terms (c) in both equations. Whenever BOTH equations have a negative constant term (−c), each equation has one positive and one negative root, so the relationship is immediately x = y or Cannot Be Determined (CND) in 2 seconds.
- If Eq I is (±, −) and Eq II is (±, −) → Mark CND immediately without calculating roots.
- If Eq I is (−, +) [roots +, +] and Eq II is (+, +) [roots −, −] → Mark x > y in 2 seconds.
Solved Exam Questions & Derivations
Solved Example 1: I. x² − 15x + 56 = 0 | II. y² + 13y + 42 = 0. Compare x and y.
- (A) x > y
- (B) x ≥ y
- (C) x < y
- (D) x = y or CND
Verified Answer: Option (A): x > y
10-Second Shortcut: Sign check only: Eq I (−, +) gives two positive roots (+8, +7); Eq II (+, +) gives two negative roots (−7, −6). Every positive number is greater than every negative number → x > y in 2 seconds.
- Inspect signs of Eq I (x² − 15x + 56 = 0): (−, +) means both roots of x are positive (+8, +7).
- Inspect signs of Eq II (y² + 13y + 42 = 0): (+, +) means both roots of y are negative (−7, −6).
- Therefore x > y for all root pairs without needing arithmetic.
Frequently Asked Questions
- Do we need to divide roots by the x² coefficient (a) when comparing x and y?
- Instead of dividing and creating fractions, cross-multiply each equation's roots by the other equation's x²/y² coefficient. That keeps all comparisons in whole integers.
- How many Quadratic Equation questions appear in IBPS PO and SBI Clerk Prelims?
- Typically 5 questions appear as a single block in the Quantitative Aptitude section, carrying 5 marks and solvable in 60–90 seconds.
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