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## Quadratic Equations: An Overview

Quadratic equations hold an important place in banking exams. The marks of 5 sure shot questions are yours if you make yourself thorough with the concepts. Some students tend to skip questions when they see a combination of exponents and fractions. But with a lot of banking exams around the corner, you do have ample time to be thorough with the basic concepts and practice it end to end. The competition is going to be intensive and with some practice, if you get an edge of 4-5 marks, it can actually make a difference in your overall score. Let’s discuss the concept below:

Quadratic equation is in the form of the expression ax^{2} + bx + c where the value of x needs to be found out. a is the coefficient of x^{2}, b is the coefficient of x and c is the constant. Have a look at the example below:

## A Question Asked Last Year

In the following questions two equations numbered (i) and (ii) are given. You have to solve both equations and Give answer

- if x > y
- if x ≥ y
- if x < y
- if x ≤ y
- If x = y or the relationship cannot be established
- (i) x
^{2}– 5x + 6 = 0

(ii) 3y^{2} + 3y – 18 = 0

The moment you get to see these types of questions, multiply the constant with the coefficient of x^{2}. In the case of x^{2} – 5x + 6 = 0, it comes to 6 (since the coefficient of x^{2} is 1). Now the next step is to think of two numbers in such a way that their product is 6 and their addition/subtraction is -5. Such 2 numbers are -2 and -3. Now, two more steps are left. First is to divide both the numbers by the coefficient of x^{2} which in this case is 1. The second step is to multiply both the numbers with -1. So the answer is 3 and 2.

The next equation can be divided by 3 resulting in y^{2} + y – 6 = 0, the product of the numbers 3 and -2 is -6 and their addition is 1. Now 3 and -2 need to be multiplied by -1 which makes the value of y as -3 and 2. It’s obvious that x ≥ y, hence option b is the answer.

## New types of Quadratic Equations Comparison Questions

These questions are easy and can be solved in seconds without picking a pen if you have done enough practice beforehand. However, the way banking exams have been surprising students, you shouldn’t be surprised if you spot questions with fractions, square roots, and two variables in a linear equation. We are giving one such example below.

## Examples:

Q1. **Directions**: In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between x and y and choose the correct option.

I. 7x + 3y = 46

II. x + y = 10

a) x > y

b) x < y

c) x = y or the relationship cannot be established

d) x ≥ y

e) x ≤ y

Ans: b

Solution:

From I:

7x + 3y = 46

7x = 46 – 3y

x = (46 – 3y)/7

From II:

x + y = 10

{(46 – 3y)/7} + y = 10 (Using (i))

46 – 3y + 7y = 70

4y = 24, y = 6

So, x = (46 – 3 × 6)/7 = 4

So, x < y.

Hence, option b.

Q2. **Directions**: In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between x and y and choose the correct option.

I) x2 – (4 + 2√3)x + 8√3 = 0

II) y2 – 3√3y + 6 = 0

a) x > y

b) x < y

c) x = y or the relationship cannot be established

d) x ≥ y

e) x ≤ y

Ans: d

Solution:

From I:

x2 – (4 + 2√3)x + 8√3 = 0

x2 – 4x – 2√3x + 8√3 = 0

x(x – 4) – 2√3(x – 4) = 0

(x – 4)(x – 2√3) = 0

x = 4, 2√3

From II:

y2 – 3√3y + 6 = 0

y2 – 2√3y – √3y + 6 = 0

y(y – 2√3) – √3(y – 2√3) = 0

(y – 2√3)(y – √3) = 0

y = 2√3, √3

So, x ≥ y.

Hence, option d.

## Mock tests aiding you in your preparation

You can practice enough beforehand to ace old and new types of questions in the actual exam. And the best tool for practice is mock tests. Platforms which offer mock tests have the experience of observing the changes in the actual tests and they prepare new questions keeping this trend in mind. Not only do mock tests give you a detailed explanation of all the questions, but they also tell you your rank among other test-takers. It also highlights your weak areas so that you can work and improve upon them. Start taking mock tests and take your preparation to the next level. All the best for your exam!

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