Decoding Quadratic Equations for IBPS Preparation

While quadratic equations are a favourite for clerical examinations, most people detest solving such confusing and nerve wracking questions. The quantitative aptitude section of the exam will most likely have a question based on quadratic equations. While you may hate this topic and wish to skip it during IBPS clerk exam preparation, if you understand the concepts clearly, they can be a breeze to solve.

Starting with the Variables

In most cases, you will be given two different quadratic equations with two variables, a basic form. When you solve these two equations, you will be able to find a relation between the two variables. Keep in mind that occasionally you may be given more variables or equations, and hence solving those is also an essential skill to master.

Take for example two variables, ‘a’ and ‘b’. They may share any kind of relationship with one being greater than the other (a>b or a<b), the two being equal (a=b) or even having no established relationship at all.

Meaning of different symbols

Before beginning with the equations themselves, here are some important symbols to know the meanings of:

‘>’

This signifies that the variable on the left side is greater than the one on the right.

‘<’
This conversely means that the variable on the right side is greater than the one on the left.

‘=’

This means that both the variables are equal.

 ‘≥’

This is indicative of the fact that the variable on the left side may be greater than or equal to the one on the right.

 ‘≤’

In a similar manner to the symbol above, it refers to the variable on the right side may be greater than or equal to the variable on the left.

General Quad Equations and their Meanings

ax² + bx + c = 0

When solving a quadratic equation, you will always get two resulting values for the equation. These two values are referred to as the roots and will always satisfy the equation. If you put the resultant values into the equation, you will always be given the answer zero.

Assuming that both the roots are known to be x=α and x=βor subsequently as (x-α) =0 and (x-β) =0, on multiplying the two equations you will get:

Step 1. (x-α)*(x-β) =0

Step 2. x²– αx- βx+ αβ=0

Step 3. x² – (α+β)x+ αβ=0

This derived equation is known as a quadratic equation that has the roots α and β.

During the course of your IBPS coaching or for your main examination you will be given questions in the following format:

Equation 1: x² – 5x + 6 = 0

Equation 2: y²+y – 6 = 0

Solution

x² – 5x + 6 = 0

Or x² – 3x – 2x + (3*2) = 0

Or x(x-3) -2(x-3) = 0

Or (x-3)(x-2) = 0

Hence x =2 or 3

y² +y – 6 = 0

Or y² +3y-2y-6 = 0

Or y (y+3) -2(y+3) = 0

Or (y+3)(y-2)=0

Hence y=-3 or 2

From the above equations we can see that x≥y.

With the basics of quadratic equations down, you can give your paper with a renewed confidence.