Quadratic Equations Questions for IBPS PO

What Is a Quadratic Equation

A quadratic equation is any equation of the form ax squared plus bx plus c equals 0, where a is not zero. In IBPS PO, you always get two equations — one in x and one in y — and you must find the roots of each, then compare them. The question never asks you to derive or prove anything. It is purely: solve and compare.

• Standard form: ax^2 + bx + c = 0
• Every quadratic has exactly two roots (can be equal)
• Roots can be integers, fractions, or equal values
• IBPS PO uses only factorable equations — no messy decimals
• You compare x vs y after finding both sets of roots

Factoring Method — The Core Skill

For IBPS PO, factoring by splitting the middle term is the fastest method. The trick: multiply coefficient of x-squared (a) with the constant (c). Then find two numbers that multiply to this product and add to the coefficient of x (b). Split the middle term using these two numbers, then group and factor. This works for almost every equation in the exam.

• Step 1: Multiply a x c to get the target product
• Step 2: Find factor pair of (a x c) that adds to b
• Step 3: Split bx into two terms using that factor pair
• Step 4: Group in pairs and take common factors
• Step 5: Roots are the values that make each bracket zero
• For simple equations where a=1, directly find factors of c that add to b

Comparing Roots — The Answer Step

After finding roots of both equations, you must compare every x value with every y value. If there are 2 roots each, you compare 4 pairs (2x2). The five possible answers are: x > y, x < y, x >= y, x <= y, or Cannot be Determined (CND). CND appears when some pairs favor x and others favor y — this is very common and a frequent trap.

• Always compare ALL pairs, not just the obvious ones
• If all x values are greater than all y values: x > y
• If some pairs are equal and rest favor x: x >= y
• If results are mixed (some x>y, some x<y): Cannot be Determined
• When both roots are equal for x and y (x1=x2=y1=y2): x = y
• Lay out roots on a number line mentally to avoid confusion

Sign Rules for Roots — Speed Hack

When you see the equation x^2 + bx + c = 0 where a equals 1, the signs of the roots follow a fixed pattern based on the signs of b and c. Memorize this pattern to guess root signs in under 5 seconds, which saves time during factoring.

• c positive, b negative: both roots are positive (e.g. x^2 - 5x + 6 = 0, roots 2 and 3)
• c positive, b positive: both roots are negative (e.g. x^2 + 5x + 6 = 0, roots -2 and -3)
• c negative, b negative: one positive one negative, larger magnitude is negative
• c negative, b positive: one positive one negative, larger magnitude is positive
• This shortcut helps you orient the number line comparison instantly

• Forgetting to check all 4 pairs when comparing roots — students often compare only the first roots of each equation and get the wrong relationship
• Sign error while splitting the middle term — especially when c is negative, the factor pair signs get mixed up
• Declaring x > y when one pair gives equality — the correct answer in that case is x >= y, not strict greater than
• Not simplifying the equation first — if there is a common factor (e.g. 2x^2 + 4x + 2 = 0, divide by 2 first) students waste time on harder numbers
• Rushing on Cannot be Determined cases — when roots of x and y overlap (e.g. x = 2,4 and y = 3,5), students pick a wrong definite answer instead of CND

• SPAM rule for root signs (when a=1): Same sign in b and c means Same-sign roots. Different signs means one root is negative, one positive.
• 4-pair rule: Two roots times two roots equals four comparisons. Never settle for less. Think of a 2x2 grid — fill all four boxes before concluding.
• Product-Sum check: After factoring, always verify using x1+x2 = -b/a and x1*x2 = c/a. Takes 5 seconds and saves you from silly errors.
• Number line trick: Plot all four roots (two x, two y) on an imaginary number line left to right. If all x dots are to the right of all y dots, x > y. If they overlap, it is CND.

• IBPS PO consistently gives 5 quadratic equation questions in one block in the Quant section. All five follow the same format — two equations, find relationship. Target all 5 correctly as this is the easiest 5-mark block in Quant.
• Recent papers (2021 to 2023) have included at least one CND question per set to trip up fast solvers. Slow down on the last comparison pair before marking.
• Difficulty is usually low to medium. Equations are designed to have integer or simple fraction roots. If your roots are coming out as ugly decimals, recheck your calculation — you likely made a sign error.
• Time target: solve each question in 25 to 35 seconds. The entire set of 5 should take under 3 minutes. If a single equation is taking more than 45 seconds, skip and come back.
• Occasionally IBPS PO gives a higher-order equation or asks for sum and product of roots directly — this happened in 2022 Prelims. Knowing the Sum = -b/a and Product = c/a formulas covers this variant without extra effort.