Quadratic Equations Questions for IBPS RRB 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. It always gives exactly two roots (answers), which can be equal, unequal, real, or imaginary. In IBPS RRB PO, both roots are always real numbers — no imaginary root questions appear. You are given two separate equations (called Equation I and Equation II), solve both, get two roots each, and then compare all combinations.

• Standard form: ax^2 + bx + c = 0
• Always gives 2 roots — call them x1, x2 for Equation I and y1, y2 for Equation II
• Roots can be integers, fractions, or decimals — IBPS mostly uses integers or simple fractions
• Sum of roots = -b/a, Product of roots = c/a (useful for quick verification)
• If discriminant (b^2 - 4ac) is negative, roots are imaginary — this does NOT appear in IBPS RRB PO

Factorization Shortcut — The Split Method

This is the only method you need for IBPS RRB PO. For ax^2 + bx + c = 0, multiply a and c to get a product P. Then find two numbers whose sum equals b and whose product equals P. Split the middle term using these two numbers, then group and factor. Practice this until it takes under 20 seconds per equation.

• Step 1: Multiply a x c to get P
• Step 2: Find two numbers that add to b and multiply to P
• Step 3: Split bx into two terms using those numbers
• Step 4: Group into two pairs and take common factors
• Step 5: Write roots — equate each bracket to zero
• If a equals 1 (most IBPS questions), skip step 1 and 3 — directly find two numbers adding to b with product c

Comparing Roots — The Answer Step

After finding roots of both equations, you compare every root of Equation I (x) with every root of Equation II (y). There are 4 comparisons total (x1 vs y1, x1 vs y2, x2 vs y1, x2 vs y2). Based on all 4 results, pick one of 5 standard answer choices. This comparison step is where most aspirants make errors — be systematic.

• x > y: all x values are strictly greater than all y values
• x < y: all x values are strictly less than all y values
• x >= y: x is greater than or equal to y in all comparisons
• x <= y: x is less than or equal to y in all comparisons
• x = y: both equations give same roots
• Cannot be determined (CND): some comparisons give x > y and others give x < y — no consistent relationship

Special Cases and Root Patterns

IBPS RRB PO frequently uses equations where one or both roots are negative, or where roots are fractions. Negative roots trip up many aspirants during comparison. Remember: -1 is greater than -5 on a number line. Also watch for equations given in non-standard forms like x^2 = 9 or (x+2)^2 = 16 — simplify first.

• x^2 = k gives roots +sqrt(k) and -sqrt(k) — both roots, do not ignore negative root
• (x + a)^2 = k gives x = -a + sqrt(k) and x = -a - sqrt(k)
• On number line: -1 > -5, so be careful comparing negative roots
• Fraction roots: 3/2 is 1.5, compare with decimals if needed
• If equation has equal roots (discriminant = 0), both roots are same — common in exam to test x >= y or x <= y outcomes

• Forgetting the negative root when solving x^2 = 9 — writing only x = 3 and missing x = -3, leading to wrong comparison
• Comparing only x1 vs y1 instead of all 4 combinations — missing one comparison that changes the answer to CND
• Sign error in split method — especially when c is negative, aspirants get the signs of the two split numbers wrong
• Marking CND when both equations give the same two roots — that is x = y, not CND
• Not simplifying the equation first — for example leaving 2x^2 = 8 as is instead of simplifying to x^2 = 4 before solving

• SPFC Rule for factorization steps: Sum, Product, Factor, Compare — Sum and Product of the two split numbers, then Factor, then Compare roots
• Number line trick: draw a quick mental line -5, -3, -1, 0, 1, 3, 5 and place all 4 roots on it — direction immediately shows x > y or x < y
• The 4-Box method: draw a 2x2 box, put x1 and x2 on top, y1 and y2 on side, fill each cell with > or < — if all cells same sign, that is your answer; if mixed, it is CND
• Analogy: Think of the two equations as two cricket teams. Roots are players. x > y means every player in Team X beats every player in Team Y. If even one player in X loses to a Y player, it is CND.

• IBPS RRB PO always gives exactly 5 quadratic equation questions in a set — all carry equal marks and same format. Solve as a group, not individually, to save time.
• Difficulty is low to medium — these are among the most scoring questions in the paper. Target all 5 correct. Spending more than 4 minutes total on this set is a red flag.
• Recent papers (2022-2024) have started including equations where a is not 1, such as 2x^2 - 7x + 6 = 0. Practice the split method for a not equal to 1.
• One question per set usually has equal roots or a CND outcome — this is the trap question. Do all 4 comparisons carefully before choosing.
• If factorization is not clicking within 15 seconds, use sum-product check: calculate -b/a and c/a, then guess factor pairs of c/a that add to -b/a. This is faster than the quadratic formula.