Quadratic Equations Questions for SBI PO

The Standard Format in SBI PO

You are given two equations — Equation I and Equation II. Solve each to get roots x and y respectively. Then compare ALL combinations of x and y and pick the correct relationship. The five answer choices are always: x > y, x < y, x >= y, x <= y, or x = y or no relation can be established. The trap is in the comparison step, not the solving step. Most aspirants lose marks here, not while finding roots.

• Always solve both equations completely before comparing.
• If Equation I gives x = 3, 5 and Equation II gives y = 4, 6 — compare each pair: (3,4), (3,6), (5,4), (5,6).
• If all comparisons point the same direction, that is your answer.
• If comparisons conflict — say x > y for one pair but x < y for another — the answer is no relation.
• Never assume one root represents all cases.

Fast Factoring Technique

For ax^2 + bx + c = 0, find two numbers that multiply to give a x c and add to give b. Split the middle term and factorise. This is the fastest method for SBI PO style equations where a, b, c are small integers. Avoid the quadratic formula — it costs 20 extra seconds per question and that adds up to 100 seconds for the full set.

• For x^2 + 5x + 6: need two numbers multiplying to 6, adding to 5. That is 2 and 3. So (x+2)(x+3)=0, roots are -2 and -3.
• For 2x^2 - 5x + 3: multiply a x c = 6. Need two numbers multiplying to 6, adding to -5. That is -2 and -3. Split: 2x^2 - 2x - 3x + 3 = 2x(x-1) - 3(x-1) = (2x-3)(x-1). Roots: 1.5 and 1.
• If c is positive: both roots share the same sign (both positive or both negative, depending on sign of b).
• If c is negative: roots have opposite signs (one positive, one negative).
• This sign rule helps you guess root pairs faster and eliminate wrong factor combinations.

Comparison Logic — The Real Differentiator

Solving is the easy part. The comparison grid is where SBI PO tests you. Think of it like a 2x2 match: x has two values, y has two values, so you have four matchups. Only if all four matchups agree can you give a definitive answer. The moment even one matchup breaks the pattern, the answer is no relation. This is the most common trap in this topic.

• Draw a quick 2x2 grid in rough: rows are x values, columns are y values.
• Put > or < in each cell. If all cells show same symbol, answer is that relation.
• If even one cell conflicts, answer is no relation.
• Watch out for equal roots: if x = y in any cell, the answer may shift from > to >= or < to <=.
• Equal roots in both equations (like x = 3, 3 and y = 3, 3) means x = y.

Special Cases to Recognise Instantly

Certain patterns repeat in PYQs. Recognising them saves 10-15 seconds per question. One common pattern is perfect square equations like x^2 - 6x + 9 = 0, which gives x = 3, 3 (equal roots). Another is difference of squares: x^2 - 16 = 0 gives x = 4 or -4. A third pattern is when one equation has all positive roots and the other all negative — comparison becomes instant without even writing the grid.

• x^2 = k type: roots are +sqrt(k) and -sqrt(k). Very common in SBI PO.
• Perfect square: (x - a)^2 = 0 gives x = a, a. One unique root repeated.
• All positive roots vs all negative roots: larger set is instantly greater.
• Equations where product of roots is negative always give one positive and one negative root — useful for quick sign identification.
• If one equation gives roots like 5, 7 and the other gives 1, 3 — no overlap, clear answer without a full grid.

• Stopping after finding roots and not doing all four comparisons — students pick the answer based on just one pair of roots and get it wrong.
• Sign errors during factoring: for x^2 - 5x + 6, factors are (x-2)(x-3), roots are +2 and +3. Students write -2 and -3 by mistake.
• Confusing >= with > when one pair gives equality: if three pairs say x > y and one pair says x = y, the answer is x >= y, not x > y.
• Using the quadratic formula for every question — it is accurate but too slow. For a 5-question set under time pressure, this alone can cost you 2 minutes.
• For equations like 2x^2 - 8 = 0, not simplifying first: divide by 2 to get x^2 = 4, so x = 2 or -2. Many aspirants apply the formula unnecessarily.

• SPCA Rule for roots: Same sign means Product is positive (check sign of Constant term). Opposite signs means product is negative. This tells you root signs before factoring.
• Grid of 4: Always make a 2x2 grid. Think of it as a mini cricket scorecard — four matchups, check winner of each. Only one-sided wins count.
• Mnemonic for answer choices: Greater, Lesser, Greater-Equal, Lesser-Equal, No Relation. Remember as GL-GLEN: G, L, GE, LE, N. Tick off which one the grid supports.
• Sum check shortcut: After finding roots, add them. If they do not match -b/a, you factored wrong. Takes 2 seconds and prevents silly errors.

• SBI PO Prelims consistently places this as a 5-question block. Target all 5 correctly — this is a full-accuracy topic, not a 3-out-of-5 topic. With practice, the full set should take under 2.5 minutes.
• SBI PO is slightly harder than IBPS PO here — expect coefficients like 3x^2 or 4y^2 more often, not just x^2 and y^2. Practice splitting middle terms for non-unity leading coefficients.
• The no relation option is used as a trap. SBI PO setters deliberately place equations where three of four comparisons point one way to tempt you. Always complete all four comparisons.
• In recent SBI PO papers, a few questions have used equations where one root is a fraction (like 3/2 or 5/3). Be comfortable comparing fractions and decimals on a number line quickly.
• Do not skip this topic even in Mains prep — occasionally Data Sufficiency questions in Mains embed a quadratic equation as a condition, and recognising the root pattern quickly adds an edge.