SBI Clerk · Bite-size lessons

Quadratic Equations

About 7 min · Numerical Ability · English

Time worked out from the lesson's 499 words at 150 words a minute, plus a minute for each question.

The format is highly standardized: you're given two quadratic equations (one in x, one in y), asked to solve both, and then compare the roots to determine the relationship between x and y.

Key ideas

• Standard form: A quadratic equation is ax² + bx + c = 0, where a, b, c are constants and a ≠ 0.
• Two roots: Every quadratic equation yields exactly two roots (which may be equal, distinct, or complex). In bank exams, roots are almost always real integers or simple fractions.
• Sum and product of roots: For x² + bx + c = 0, the sum of roots = −b and the product of roots = c. This helps verify your factorization.
• Factorization method: Split the middle term into two parts whose product equals a×c and whose sum equals b. This is the fastest solving approach for exam questions.
• Comparison logic: After finding roots of both equations, compare all possible pairs. The relationship depends on whether one variable's roots are consistently greater, smaller, or overlap with the other's.

Watch out for

• Sign errors with negative coefficients: When b and c are both positive in x² + bx + c = 0, both roots are negative (sum = −b is negative, product = c is positive). Students often forget the negative sign when writing final roots. → Always check: plug roots back to verify sum and product.
• Comparing only one pair of roots: Students find x = 3, y = 4 and conclude x < y, ignoring that x might have another value that's greater than y. → Always compare all four possible pairs (x₁ vs y₁, x₁ vs y₂, x₂ vs y₁, x₂ vs y₂).
• Confusing ≥ with > on boundary cases: When one root of x equals one root of y, but other comparisons are strict, the answer is ≥ or ≤, not > or <. → If there's any equality, use ≥ or ≤; pure inequalities only when no overlap exists.

Quick reference

• Split middle term: find two numbers with product = a×c and sum = b
• Negative b and positive c → both roots positive
• Positive b and positive c → both roots negative
• Negative c → roots have opposite signs
• Compare all four pairs; consistent inequality → definite answer; overlap → cannot determine

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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.

Read the full noteFlashcards for this topic