The worked question on this page is original educational practice. It is not represented as a question from an official previous-year examination paper.
01 / UNDERSTANDING
Review the question
Create original pairs of quadratics with always-less, always-greater and mixed outcomes. Require root sets in the working so an unsupported relation can be traced to the omitted pairing.
02 / UNDERSTANDING
The concept in context
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
Learn from the attempt
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.
