Quadratic Equation Questions for IBPS RRB, PO, and Other Bank Exams: In the realm of competitive banking exams like IBPS RRB, IBPS PO, SBI PO, and other similar tests, quantitative aptitude plays a vital role in determining a candidate’s overall score. Among the many topics under this section, quadratic equations is one of the most frequently asked and scored topics.
If prepared well, quadratic equation questions can be solved in under a minute, helping aspirants save crucial time for lengthier problems. Let’s explore this topic in detail, along with practice questions and preparation tips.
What Is a Quadratic Equation?
A quadratic equation is a second-degree equation of the form: ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0
Where:
- aaa, bbb, and ccc are real numbers, and
- a≠0a \neq 0a=0
The equation will always have two roots (real or imaginary), and your task is usually to find and compare these roots with another equation.
Why Are Quadratic Equations Important in Bank Exams?
Here’s why you must pay special attention to this topic:
- High frequency: Almost every banking prelims exam includes 5 questions from quadratic equations.
- Time-efficient: Once you master solving them, you can finish all 5 questions in under 3–4 minutes.
- Conceptually simple: Most questions require factoring or basic comparison.
Common Question Pattern for Quadratic Equations
In exams, you’re typically given two quadratic equations, one in variable xxx and one in yyy. You’re then asked to compare the roots and choose the correct relation: x2+5x+6=0andy2+7y+10=0x^2 + 5x + 6 = 0 \quad \text{and} \quad y^2 + 7y + 10 = 0x2+5x+6=0andy2+7y+10=0
Options are usually
- x>yx > yx>y
- x<yx < yx<y
- x≥yx \ge yx≥y
- x≤yx \le yx≤y
- Relationship can’t be determined
How to Solve Quadratic Equation Questions?
To solve the quadratic equations step-by-step, follow these steps:
- Factor both equations, if possible.
- Find the roots of each equation.
- Compare every root of xxx with every root of yyy.
- Choose the correct option based on the comparison.
Tips and Tricks for Solving Quadratic Equations
- Always try simple factoring first: most exam questions are designed to be factorable.
- Use the quadratic formula only when factoring is hard.
x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}x=2a−b±b2−4ac
- Remember identities, such as a2−b2=(a+b)(a−b)a^2 – b^2 = (a + b)(a – b)a2−b2=(a+b)(a−b) for quick simplification.
- Practice inequality comparisons for root analysis.
Solved Quadratic Equation Questions
Q1.
Solve:
x² + 7x + 12 = 0
y² + 9y + 20 = 0
Step 1: Factor both equations
x² + 7x + 12 = (x + 3)(x + 4) → x = -3, -4
y² + 9y + 20 = (y + 4)(y + 5) → y = -4, -5
Step 2: Compare values
x = -3, -4
y = -4, -5
Compare:
-3 > -4 and -4 = -4 → So x ≥ y
Answer: x ≥ y
Q2.
Solve:
x² – 11x + 28 = 0
y² – 13y + 42 = 0
Step 1: Factor both equations
x² – 11x + 28 = (x – 4)(x – 7) → x = 4, 7
y² – 13y + 42 = (y – 6)(y – 7) → y = 6, 7
Step 2: Compare values
x = 4, 7
y = 6, 7
4 < 6, 7 = 7 → x ≤ y
Answer: x ≤ y
Q3.
Solve:
x² – 6x + 9 = 0
y² – 4y + 4 = 0
Step 1: Recognise perfect squares
x² – 6x + 9 = (x – 3)² → x = 3
y² – 4y + 4 = (y – 2)² → y = 2
Step 2: Compare values
x = 3
y = 2
3 > 2
Answer: x > y
Q4.
Solve:
x² + 3x – 10 = 0
y² + 5y – 14 = 0
Step 1: Factor
x = 2, -5
y = 2, -7
Step 2: Compare
One value is equal (x = y = 2), other x > y (-5 > -7)
→ Mixed results
Answer: Cannot be determined
Q5.
Solve:
x² + 5x + 6 = 0
y² + 6y + 9 = 0
Step 1: Factor
x² + 5x + 6 = (x + 2)(x + 3) → x = -2, -3
y² + 6y + 9 = (y + 3)² → y = -3
Step 2: Compare
x = -2, -3
y = -3
→ -2 > -3 and -3 = -3 → x ≥ y
Answer: x ≥ y
Q6.
Solve:
x² – 10x + 21 = 0
y² – 7y + 10 = 0
Step 1: Factor
x = 3, 7
y = 2, 5
Step 2: Compare
3 > 2 and 7 > 5 → x > y
Answer: x > y
Q7.
Solve:
x² – 8x + 15 = 0
y² – 7y + 12 = 0
Step 1: Factor
x = 3, 5
y = 3, 4
Step 2: Compare
3 = 3, 5 > 4 → x ≥ y
Answer: x ≥ y
Q8.
Solve:
x² – x – 20 = 0
y² + 2y – 24 = 0
Step 1: Factor
x = 5, -4
y = 4, -6
Step 2: Compare
One x = 5 > y = 4
Other x = -4 > y = -6
→ Both x values > y values
Answer: x > y
Q9.
Solve:
x² – 2x – 35 = 0
y² – 7y + 10 = 0
Step 1: Factor
x = 7, -5
y = 2, 5
Step 2: Compare
x = 7 > 5, -5 < 2 → One x > y, one x < y
Answer: Cannot be determined
Q10.
Solve:
x² + 10x + 24 = 0
y² + 9y + 20 = 0
Step 1: Factor
x = -4, -6
y = -4, -5
Step 2: Compare
x = -4, -6
y = -4, -5
→ One x = y, one x < y → mixed
Answer: Cannot be determined
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