IBPS Clerk · Bite-size lessons
Quadratic Equations
About 6 min · Numerical Ability · English
Time worked out from the lesson's 407 words at 150 words a minute, plus a minute for each question.
Quadratic equations in IBPS Clerk Prelims follow a fixed, predictable pattern: you receive two equations (one in x, one in y), solve both, then compare the roots to determine the relationship between x and y.
Key ideas
- Standard form: A quadratic equation is written as ax² + bx + c = 0, where a, b, c are constants and a ≠ 0.
- Roots: The values of x (or y) that satisfy the equation. Each quadratic has exactly two roots (which may be equal or distinct).
- Sum of roots = -b/a; Product of roots = c/a. Use these to verify your factorization quickly.
- Factorization method: Split the middle term into two parts whose product equals a × c and whose sum equals b.
- Sign convention for comparison: After finding both roots of each equation, compare all possible pairs and decide the universal relationship.
Watch out for
- Ignoring negative roots in comparison: Students forget that -3 > -5. Fix: Draw a number line mentally; numbers increase as you move right.
- Assuming single overlap means x = y: If x = 4 and y = 4 appear, but other values differ, the answer is ≥ or ≤, not strictly equal. Fix: Compare ALL root pairs.
- Sign errors during factorization: When c is positive and b is negative, both factors are negative. When c is negative, factors have opposite signs. Fix: Check product and sum before finalizing.
Quick reference
- Factorize both equations → Get two roots each → Compare all four pairs
- Sum of roots = -b/a, Product of roots = c/a (use to verify)
- All x > all y → Answer: x > y
- All x < all y → Answer: x < y
- Some equal, rest one-sided → Answer: x ≥ y or x ≤ y
Check yourself: 3 questions
1. I. x² - 11x + 28 = 0 II. y² - 15y + 56 = 0 What is the relation between x and y?
2. I. 2x² - 13x + 21 = 0 II. 2y² - 19y + 44 = 0 What is the relation between x and y?
3. I. x² - 9x + 20 = 0 II. y² - 13y + 42 = 0 What is the relation between x and y?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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