# Basics of Quadratic Equations for Bank Exams

By Jyoti Bisht|Updated : June 28th, 2021

Hello aspirants,

Almost every banking test includes a section on quadratic equations since it is one of the most important topics. Many Banking and Insurance Examinations include a series of 4-5 questions on quadratic equations in the Quantitative Aptitude exam. Two quadratic equations in two separate variables are provided in most cases.

Hello aspirants,

Almost every banking test includes a section on quadratic equations since it is one of the most important topics. Many Banking and Insurance Examinations include a series of 4-5 questions on quadratic equations in the Quantitative Aptitude exam. Two quadratic equations in two separate variables are provided in most cases.

To find the relationship between the two variables, we must solve both quadratic equations.

Let's say we have two variables, x and y. Any of the following relationships can exist between the variables:

• x>y
• x<y
• x=y or relation can’t be established between x & y
• x≥y
• x≤y

## What is the meaning of different symbols?

Before getting deep into the quadratic equations, let us try to understand the meaning of the basic operations used in finding the relationship between the variables –

(1) ‘>’ symbol: This symbol indicates that the variable on the left side is definitely greater than the variable on the right side of the symbol.

For example, x>y means x is definitely greater than y.

(2) ‘<’ symbol: This symbol indicates that the variable on the left is definitely smaller than the variable on the right side of the symbol.

For example x<y means x is definitely smaller than y.

(3) ‘=’ symbol: This symbol indicates that the variable on the left side is equal to the variable on the right side of the symbol.

For example, x=y means x is definitely equal to y.

(4) ‘≥’ symbol: This symbol indicates that the variable on the left side is either greater than or equal to the variable on the right side of the symbol.

For example, x≥y means x is either greater than y or equal to y.

(5) ‘≤’ symbol: This symbol indicates that the variable on the left side is either smaller than or equal to the variable on the right side of the symbol.

For example, x≤y means x is either smaller than y or equal to y.

### General Form of a Quadratic Equation

ax2 + bx + c = 0

The maximum power of the variable in a quadratic equation is always ‘2', which means we will always get the ax2 term in a quadratic equation.

Or we can say that b can be 0, c can be 0 but a will never be 0.

We will always receive exactly two values of a quadratic equation when we solve it. The roots of the equation are these two values. The equation is always satisfied by the roots of the equation. In the event of doubt, we can double-check the solution by re-entering the values into the equation. Our roots are right if the equation turns out to be zero.

Let us see how we can obtain a quadratic equation if we know the roots so that we will get a very clear concept of the basic formation of a quadratic equation.

Suppose we know both the roots as x=α and x=β.

Or we can say that (x-α)=0 and (x-β)=0

If we multiply both the equations, we will get

(x-α)*(x-β)=0

x2- αx- βx+ αβ=0

x2 - (α+β)x+ αβ=0

The obtained equation is a quadratic equation having roots α and β.

## Methods of finding roots of a quadratic equation

First method:

ax2+ bx + c = 0

or, x2+(b/a)x+(c/a)=0

Now let's compare the two equations that have been indicated.

After comparison, we will get:

(α+β) = -(b/a)

αβ = c/a

#### Example:

x2+9x+20=0

a=1,b=9,c=20

(α+β) = -9/1 = -9

αβ = 20/1 = 20

So, now we have to think which two numbers multiplication gives us 20 and their addition gives -9.

The answer is -5 and -4. So these two are the roots or solution for equation x2+9x+20=0.

Second method:

x2+(4+5)x+(4*5)=0

x2+4x+5x+4*5=0

x(x+4)+5(x+4)=0

(x+4)(x+5)=0

So x=-4 and x=-5

Third method:

The following formula can be used to discover the roots of a quadratic equation:

x=[-b± √{b2-4ac}]/2a

x=[-9± √{92-4*1*20}]/2*1

x=[-9± √{81-80}]/2

x=[-9± √1]/2

x=[-9± 1]/2

x=(-9+1)/2 and x=(-9-1)/2

x=-8/2 and x=-10/2

x=-4 and x=-5

Direction: In the following question two equations numbered I and II are given. You have to solve both the equations and answer the question.

1. I.X2 – 37X + 210 = 0
II. Y2 – 47Y + 280 = 0

A. X > Y
B. X ≥ Y
C. Y > X
D. Y ≥ X
E. X = Y OR the relationship cannot be established

X2 – 37X + 210 = 0
X2 – 30X –7X + 210 = 0
X(X – 30) – 7(X – 30) = 0
(X – 30)(X – 7) = 0
X = 7, 30

Y2 – 47Y + 280 = 0
Y2 – 40Y – 7Y + 280 = 0
Y(Y – 40) –7(Y – 40) = 0
(Y – 7)(Y – 40)=0
Y = 7, 40
X=30 is greater than Y=7 as well as less than Y=40
So, the relationship cannot be established

Direction: In the following question, there are two equations. Solve the equations and answer accordingly:

1. I: x= ()3
II: 30y= 750

A. x > y
B. x < y
C. x ≥ y
D. x ≤ y
E. x = y OR No relation can be established(CND)

x3=()3
x3=(
x3=216
x=
x=6
30y2=750
y2=750÷30
y2=25
y=√25
y= ±5
x>y

Direction: In the following question two equations are given in variables X and Y. You have to solve these equations and determine relation between X and Y.

1. √(x + 20) = √256 – √121
y+ 584 = 705

A. x > y
B. x < y
C. x ≥ y
D. x ≤ y
E. x = y OR No relation can be established(CND)

√(x + 20)=√256 – √121
√(x+20)=16-11
√(x+20)=5
x+20=52
x+20=25
x=25-20
x=5
y2+584=705
y2=705-584
y2=121
y = -11, 11
No relationship can be established between 'x' & 'y'.

Directions: In each of the following questions two equations (I) and (II) are given. Solve both the equations and give an answer.

1. (I) 3x2+ 8x + 4 = 0
(II) 4y2 - 19y + 12 = 0.

A. x > y
B. x ≥ y
C. x < y
D. x ≤ y
E. x = y or relationship cannot be established

(3x+2) (x+2)
Solving we get x= -2/3 or -2
(4y-3) (y-4)
y= 3/4 or 4
y>x

Direction: In the following question two equations numbered I and II are given. You have to solve both the equations and mark the correct answer.

1. I. X- 11x + 28 = 0
II. y+ y - 30 = 0

A. x > y
B. x ≥ y
C. x < y
D. x ≤ y
E. X = Y or the relationship cannot be established

I. X2-11x+28=0
X2-7x-4x+28=0
(x-7)(x-4)=0
x = 4, 7
II. y2+y-30=0
y2+6y- 5y-30=0
(y+6)(y+5)=0
y = 5, -6
Relationship cannot be established

Any of these three methods can be used to find out the roots of a quadratic equation.

As we can see in the number line that x and y values have a common area so no relation can be established between x & y.

Key points related to Quadratic Equations:

1. Find the roots of both equations one at a time using one of the three approaches.
2. Draw the roots on the number line after you've discovered them.
3. There are 5 choices on the number line:
• If x comes to an end before y begins, the relationship will be x<y.
• If y comes to an end before x, the relationship will be y<x.
• If y begins at the same place where x finishes, the connection will be x≤y.
• If x begins and finishes precisely where y does, the relationship will be x≥y.
If y begins before x ends or vice versa, no relationship between x and y can be constructed.
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Quadratic equation questions do come in these bank exams too so it's worth preparing this topic for sure.

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write a comment

jinde mallayyaJul 12, 2020

Thank you

AnandSep 28, 2020

Thanks

Raje Pravin HakeSep 28, 2020

Thanks

Dhanusha MeesalaSep 29, 2020

Thankyou so much sir 🙂🙂

AryanOct 19, 2020

Ok thanks

स्वरूपJun 28, 2021

हेलो

Devendra GautamJun 30, 2021

Best

Hiiii
Thank you for the basics... These are very fundamental to solve quadratic problems yet important to revise and solve as many as we can.
🙏🙌

Harriat GraceAug 6, 2021

U

## FAQs

• Almost every banking exam like SBI, IBPS, GIC, NABARD, etc includes a section on quadratic equations since it is one of the most important topics.

• The weightage of quadratic equation questions in Bank Exam 2021 carries 4-5 questions on quadratic equations in the Quantitative Aptitude exam.

• The type of relationship between the variables in Quadratic Equation questions are-

• x>y
• x<y
• x=y or relation can’t be established between x & y
• x≥y
• x≤y

• The general form of Quadratic Equation is ax2 + bx + c = 0.

• The other method to solve quadratic equation in Quantitative 2021 Exam is x=[-b± √{b2-4ac}]/2a.

• This symbol indicates that the variable on the left side is either greater than or equal to the variable on the right side of the symbol.

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