IBPS RRB Quadratic Equations: Root Comparison Method with Worked Examples

Compare roots in IBPS RRB quadratic equation questions quickly: factorisation, sign rules, the "no relation" case, worked examples and a mock practice plan.

What the question is really asking

In IBPS RRB and other bank prelims, quadratic equation questions give two equations, one in x and one in y, and ask for the relation between x and y: x > y, x < y, x ≥ y, x ≤ y, x = y, or no relation. You are not asked for the roots themselves. You are asked whether every root of one equation stands in the same relation to every root of the other.

The examples below are original practice questions. Check the current pattern and syllabus in the official notification on the IBPS website. Scholareum does not predict the number of such questions in any shift.

Step 1: Factorise using sum and product

For x² + bx + c = 0, find two numbers whose product is c and whose sum is b; the roots are those numbers with signs reversed. For ax² + bx + c = 0, split the middle term using two numbers whose product is a × c.

Step 2: Use the sign shortcut before solving

+b, +c: both roots are negative.
−b, +c: both roots are positive.
c negative: one root is positive and one is negative.

If both x-roots are positive and both y-roots are negative, then x > y immediately, without finding any value. Use this check first; it saves time on many questions.

Step 3: Compare all four pairs

With two roots each, there are four comparisons. Write them, then decide:

All ">" gives x > y; all "<" gives x < y.
A mix of ">" and "=" gives x ≥ y; a mix of "<" and "=" gives x ≤ y.
Any mix of ">" and "<" gives no relation (often printed as "relationship cannot be established").

Worked example 1

I. x² − 7x + 12 = 0 → (x − 3)(x − 4) = 0 → x = 3, 4 II. y² − 11y + 30 = 0 → (y − 5)(y − 6) = 0 → y = 5, 6

Every x is smaller than every y. x < y.

Worked example 2: the equal root

I. x² + 5x + 6 = 0 → x = −2, −3 II. y² + 3y + 2 = 0 → y = −1, −2

Pairs: −2 vs −1 (<), −2 vs −2 (=), −3 vs −1 (<), −3 vs −2 (<). One "=" with the rest "<" gives x ≤ y. Missing the equal pair and answering x < y is the most common error here.

Worked example 3: square roots

I. x² = 16 → x = +4 or −4 II. y² − 8y + 16 = 0 → (y − 4)² = 0 → y = 4

Pairs: 4 vs 4 (=), −4 vs 4 (<). x ≤ y. Remember that x² = 16 has two roots, but y = √16 would have only +4.

Worked example 4: no relation

I. 2x² − 7x + 3 = 0 → (2x − 1)(x − 3) = 0 → x = 0.5, 3 II. y² − 4y + 3 = 0 → y = 1, 3

Pairs: 0.5 < 1, 0.5 < 3, 3 > 1, 3 = 3. Both "<" and ">" appear, so no relation can be established.

Common mistakes

Reversing signs incorrectly. The factor (x + 3) gives the root −3.
Dropping the negative root of x² = k.
Checking only the largest roots. All four pairs matter.
Forgetting the coefficient of x² when splitting the middle term; multiply a × c first.
Spending too long. If factorisation is not obvious in 20 seconds, use the quadratic formula or move on and return later.

A 10-day practice plan

Days 1–3: 25 single-equation factorisations daily, including ax² + bx + c forms.
Days 4–6: Paired-equation sets with the sign shortcut written before solving.
Days 7–8: Timed sets of 10 pairs in 5 minutes; log every "≥/≤" mistake.
Days 9–10: Take full mocks from the IBPS RRB test series or the IBPS RRB Officer Scale-I & Assistant pack and review accuracy in the quantitative section.

Frequently asked questions

Are quadratic questions good to attempt first? For many candidates they are among the quickest marks in quantitative aptitude. Use your own mock analytics to decide.

What if the equations have irrational roots? Exam questions usually factorise neatly. If they do not, compare using approximate values from the quadratic formula.

Where can I find more banking practice? Browse all mock tests, the SBI Clerk full-length pack, and the exam calendar — confirming dates on the official IBPS site.

Related reading: SBI Clerk inequality worked examples and IBPS Clerk simplification and approximation methods. Unlock every mock with Scholareum Pro.