Study Material — 9 PYQs (2019–2019) · Concept Notes · Shortcuts
IBPS RRB PO Quadratic Equations is a frequently tested subtopic — 9 previous year questions from 2019–2019 papers are included below with concept notes, key rules and shortcut tricks.
IBPS RRB PO Quadratic Equations — Past Exam Questions
9 questions from actual IBPS RRB PO papers · all shown free · click option to reveal solution
Exam Q 12019Previous Year Pattern
If x² - 7x + 12 = 0, find the sum of the roots of the equation.
Exam Q 22019Previous Year Pattern
The quadratic equation whose roots are 4 and -2 is:
Exam Q 32019Previous Year Pattern
If one root of the equation x² - 4x + p = 0 is 3, find the value of p and the other root.
Exam Q 42019Previous Year Pattern
The product of the roots of the equation 3x² + 6x - 9 = 0 is:
Exam Q 52019Previous Year Pattern
If the roots of the quadratic equation 2x² - 8x + k = 0 are equal, find the value of k.
Exam Q 62019Previous Year Pattern
The quadratic equation x² - (p+q)x + pq = 0 has roots p and q. If p = 3 and the sum of roots is 8, find q.
Exam Q 72019Previous Year Pattern
A quadratic equation x² + bx + c = 0 has roots that differ by 5. If the sum of roots is 7, find the value of c.
Exam Q 82019Previous Year Pattern
If α and β are roots of x² - 6x + k = 0, and γ and δ are roots of x² - 12x + m = 0, and if α, β, γ, δ are in arithmetic progression (in that order), then k + m equals:
Exam Q 92019Previous Year Pattern
The quadratic equation x² + bx + c = 0 has roots r and s. A new equation is formed by replacing each root with its square: x² - (r² + s²)x + r²s² = 0. If the original equation has b = -5 and c = 6, then the constant term of the new equation is:
Concept Notes
Quadratic Equations— Rules & Concept
Core ConceptRead this first — the foundation of the topic
Quadratic Equations are polynomial equations with the highest degree of 2. They form the backbone of algebra questions in SSC CGL and appear in almost every exam paper. A quadratic equation has the standard form ax² + bx + c = 0, where 'a' cannot be zero. Core Properties and Rules:
Every quadratic equation has exactly two roots (solutions). These roots can be real and equal, real and unequal, or imaginary. The nature of roots depends on the discriminant (b² - 4ac). When discriminant > 0, roots are real and unequal. When discriminant = 0, roots are real and equal. When discriminant < 0, roots are imaginary.
Formula BlockMemorise — at least one formula appears in every paper
Quadratic Formula: x = [-b ± √(b² - 4ac)] / 2a
Sum of roots = -b/a
Product of roots = c/a
If roots are α and β, then equation is: x² - (α + β)x + αβ = 0
Exam PatternsWhat examiners ask — read before attempting PYQs
SSC CGL typically asks 2-3 questions on quadratic equations. Common question types include finding roots, determining nature of roots, forming equations from given roots, and word problems leading to quadratic equations. Questions often involve finding maximum/minimum values or solving practical problems.
ShortcutsUse these to save 30–60 seconds per question
#1 - Middle Term Splitting:
For ax² + bx + c = 0, find two numbers whose product = ac and sum = b. Split the middle term using these numbers. This method is faster than the quadratic formula for most SSC questions.
Shortcut Trick #2 - Perfect Square Recognition:
If b² = 4ac, the equation is a perfect square.
The root is -b/2a (repeated twice). This saves calculation time.
Worked ExampleSolve this step-by-step before moving on
1
Step 1
Identify a = 2, b = -7, c = 3
2
Step 2
Find ac = 2 × 3 = 6
3
Step 3
Find two numbers whose product = 6 and sum = -7
These are -6 and -1 (since -6 × -1 = 6 and -6 + (-1) = -7)
4
Step 4
Rewrite: 2x² - 6x - x + 3 = 0
5
Step 5
Factor: 2x(x - 3) - 1(x - 3) = 0
6
Step 6
(2x - 1)(x - 3) = 0
7
Step 7
Roots are x = 1/2 and x = 3
Worked Example 2:
Find the equation whose roots are 3 and -2.
1
Step 1
Sum of roots = 3 + (-2) = 1
2
Step 2
Product of roots = 3 × (-2) = -6
3
Step 3
Using x² - (sum of roots)x + (product of roots) = 0
4
Step 4
Required equation: x² - x - 6 = 0
Shortcut Trick #3 - Vieta's Relations:
Instead of finding individual roots, use sum and product formulas directly. This is especially useful when questions ask about expressions involving roots without finding the actual roots.
Common Trap - The #1 Mistake:
Students often forget to check if 'a' equals zero. If a = 0, the equation becomes linear (bx + c = 0), not quadratic. Always verify that the coefficient of x² is non-zero before applying quadratic methods. Another common error is sign mistakes while applying the quadratic formula, especially with the discriminant calculation.
Exam Strategy:
For SSC CGL, master middle term splitting first as it's faster than the quadratic formula. Practice identifying perfect squares quickly. Word problems often lead to quadratic equations, so focus on translation skills. Time management is crucial - spend maximum 2 minutes per quadratic equation question.
Key Points to Remember
Standard form: ax² + bx + c = 0 where a ≠ 0
Discriminant = b² - 4ac determines nature of roots
Sum of roots = -b/a, Product of roots = c/a
Middle term splitting is faster than quadratic formula for most SSC questions
If b² = 4ac, equation is perfect square with root = -b/2a
Every quadratic equation has exactly two roots
Roots can be real unequal, real equal, or imaginary
For forming equation from roots: x² - (sum)x + (product) = 0
Use Vieta's relations when questions involve expressions of roots
Always verify coefficient of x² is non-zero before applying quadratic methods
Exam-Specific Tips
Discriminant > 0 means real and unequal roots
Discriminant = 0 means real and equal roots
Discriminant < 0 means imaginary roots
Maximum value of quadratic expression ax² + bx + c occurs at x = -b/2a when a < 0
Minimum value of quadratic expression ax² + bx + c occurs at x = -b/2a when a > 0
If roots are reciprocals of each other, then a = c