Quadratic Equations Questions for RBI GRADE B

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 has exactly two roots (solutions), which can be real or complex, equal or unequal. In bank exams, the roots are almost always integers or simple fractions, so factorisation is faster than the formula.

• Standard form: ax^2 + bx + c = 0
• Two roots always exist (counting multiplicity)
• For RBI Grade B, roots are typically integers between -10 and 10
• The question asks: is x > y, x < y, x = y, x >= y, x <= y, or relationship cannot be determined
• Two separate equations are given — one for x, one for y — and you compare their root sets

Factorisation Method (Primary Exam Technique)

Split the middle term. Find two numbers whose sum equals b and whose product equals a times c. This is the fastest method for bank exam questions. Once you have the two factors, set each to zero to get the roots. Write roots clearly before comparing — this is where most errors happen.

• Step 1: Multiply a and c to get the target product
• Step 2: Find two numbers that add to b and multiply to (a times c)
• Step 3: Split bx into two terms, then factor by grouping
• Step 4: Write both roots explicitly with their signs
• Step 5: Compare ALL combinations of x-roots with y-roots

Sign Rule Shortcut for Quick Factorisation

When the leading coefficient a equals 1, the signs of the roots follow a simple pattern based on the signs of b and c. Memorise this as a reflex — it saves 20-30 seconds per question. This works only when a = 1; for a not equal to 1, divide through or use grouping.

• c positive, b negative: both roots are negative in sign-flip sense — both roots are positive (e.g., x^2 - 5x + 6: roots +2, +3)
• c positive, b positive: both roots are negative (e.g., x^2 + 5x + 6: roots -2, -3)
• c negative, b positive: one root positive larger, one root negative smaller (e.g., x^2 + x - 6: roots +2, -3)
• c negative, b negative: one root negative larger magnitude, one positive (e.g., x^2 - x - 6: roots +3, -2)
• Analogy: think of c as telling you if roots are same sign (c positive) or opposite sign (c negative)

Comparing Roots and Choosing the Right Answer

After finding roots of x-equation and y-equation, you must compare every x-root with every y-root. With two roots each, that is 4 comparisons. If all x values are greater than all y values, answer is x > y. If mixed results, the answer is cannot be determined. Be systematic — write roots on a number line mentally.

• List x roots as a set, list y roots as a set
• Check: is every x greater than every y? Then x > y
• Check: is every x less than every y? Then x < y
• If roots overlap or ordering flips, mark cannot be determined
• Equal roots case: if all values are equal, answer is x = y; if some equal some greater, use x >= y or x <= y accordingly
• Never skip writing out both roots — mental shortcutting causes sign errors

Vieta Formulas as a Verification Tool

After factorising, quickly verify using Vieta formulas. Sum of roots should equal -b/a and product should equal c/a. This takes 5 seconds and catches sign mistakes before you move to comparison. In exams, one wrong sign in a root flips the entire answer.

• For x^2 - 5x + 6: sum = 2+3 = 5 = -(-5)/1. Product = 2x3 = 6 = 6/1. Verified.
• For 2y^2 + y - 6: sum = 1.5 + (-2) = -0.5 = -1/2. Product = 1.5 x (-2) = -3 = -6/2. Verified.
• Use this as a 5-second sanity check, not as a solving method

• Sign error on roots: writing x = +2 instead of x = -2 after solving (x+2)(x-3) = 0. Remember: if the factor is (x+2), the root is x = -2, not +2.
• Comparing only one root instead of all combinations: comparing just the first x-root with the first y-root and jumping to a conclusion — you must check all four pairings.
• Not simplifying the equation first: if the equation is 2x^2 - 10x + 12 = 0, divide by 2 first to get x^2 - 5x + 6 = 0. Skipping this step makes factorisation harder and wastes time.
• Marking cannot be determined too quickly or too late: if one x-root equals a y-root but others differ, you may need >= or <= not cannot be determined. Read all five answer options carefully.
• Using the quadratic formula for every problem: it is slow and error-prone under exam pressure. Use it only when the discriminant is not a perfect square or factorisation clearly fails.

• SPCO rule for sign of roots when a=1: Same sign in roots when C is pOsitive; Opposite signs when C is negative. Then b tells you which direction (both positive or both negative in the same-sign case).
• SUM-PRODUCT double check mantra: after factorising, always whisper S equals minus b over a and P equals c over a — takes 5 seconds, saves 2 marks.
• Number line mental image: plot both sets of roots on an imaginary number line. If one entire cluster sits to the right of the other cluster, that cluster is greater. Mixed clusters mean cannot be determined.
• Factor bracket root flip: whatever number is inside the bracket gets its sign flipped to become the root. (x - 3) gives root +3; (x + 3) gives root -3. Think of it as the bracket lying — it always says the opposite.

• RBI Grade B Phase 1 typically has a block of 5 quadratic comparison questions. They appear together and follow identical format. Budget 3.5 to 4 minutes for all five — roughly 45 seconds each.
• Recent papers have included cases where one or both roots are fractions (like 3/2 or -5/3) to test if candidates can still compare accurately. Practice at least 10 such questions with fractional roots.
• The answer option cannot be determined is used more frequently in harder question sets. Examiners create equations where one x-root is between the two y-roots intentionally. Always check all 4 pairings.
• Occasionally a quadratic appears inside a Data Sufficiency question in Phase 1 or a word problem in Phase 2 ESI/FM. The underlying mechanics are identical — just solve for roots and use them as values.
• Do not spend time on factorisation if the discriminant is clearly not a perfect square — use the formula, get decimal roots, and compare. This is rare but happens once in 2-3 exam cycles.