This Bankers Tutorial article is independent educational material. Examples are illustrative, and changing rules or examination requirements should be checked at the official source.
01 / UNDERSTANDING
Understand the idea
Listing two small sets can be more reliable than performing a complicated comparison in your head. The notation protects against losing a valid value while trying to save a few seconds.
02 / UNDERSTANDING
The concept in context
A quadratic equation may have two roots, one repeated root or no real roots. In basic comparison questions, factorisation often gives the candidate values quickly. Keep the signs consistent: if a factor is x minus three, setting it to zero gives x equal to three, not minus three.
Comparing variables requires every allowed pairing unless additional conditions select one root. If x has values two and five while y has values three and four, some pairings place x below y and others above it. An answer based on just one pairing ignores the information contained in the full solution sets.
03 / UNDERSTANDING
A worked learning case
Original educational case. The original equation x² − 7x + 12 = 0 factors as (x − 3)(x − 4), so x is 3 or 4. If y² − 11y + 30 = 0, y is 5 or 6. Every possible x is less than every possible y, so x < y follows without choosing a particular pair.
ORIGINAL EDUCATIONAL PRACTICE
Try it before you check.
Original practice: Find all real roots of x² − 5x + 6 = 0.
Show the answer and reasoning
x = 2 or x = 3.
The factors are (x − 2)(x − 3), because the constants multiply to 6 and their negative sum is −5. A product is zero when at least one factor is zero, giving the two roots. Substituting both values into the original equation verifies that neither solution has been lost.
Two traps to watch for.
- Reversing root signs when reading factors.
- Comparing only one selected root from each equation.
YOUR TOPIC-SPECIFIC LEARNING MAP
Turn understanding into practice
Factor and list all roots.
Substitute roots back into the equation.
Check every allowed comparison pairing.
Explain the idea, apply it to a new situation, then check what changed in your reasoning.
BANKERS TUTORIAL · SOURCE NOTES
Keep the source alongside your notes.
Official links provide subject context and authoritative reference material. This guide’s explanation, scenario and question are original Bankers Tutorial learning content.
- sbi.bank.in https://sbi.bank.in/web/careers/current-openings
- sbi.bank.in https://sbi.bank.in/webfiles/uploads/files_2627/09/SBI_JA-Customer_Support_Sales-IH_Pre-2026-27_Eng.pdf
For SBI preparation, check the current official notice before relying on changing dates, rules or examination requirements.
