How to Solve Quadratic Equations for Bank PO | Know Here

An equation of the form ax²+bx+c=0 is called quadratic equation where a= coefficient of x², b= coefficient of x and c= constant. A Quadratic Equation ax²+bx+c=0  always have two solutions.

Discriminant Method to find the Value of x:

x = (-b±√(b^2-4ac))/2a

Eg- 3x²+14x+8=0

Here a=3, b=14, c=8

x = (-b±√(b^2-4ac))/2a 

= (-14±√(14^2-4✕3✕8))/(2✕3)

= (-14±√(196-96))/6

=(-14±√(100))/6

=(-14±10)/6

Take +ve sign, x=(-14+10)/6 = -4/6 = -0.226

Take -ve sign , x=(-14-10)/6 = -24/6 = -4

Factorization Method to find the value of x:

ax²+bx+c=0 

acx² = Multiplication of factor bx which must result bx on addition

Eg- 3x²+14x+8=0

Here a=3, b=14, c=8

acx²=8✕3x² = 24x²

Now see the factor of 14x which gives 24x² i.e. 12x✕2x

You also need to see that addition of the factor of 14x must result 14x and multiplication mus result 24x²

Here factor of 14x are 12x and 2x

On addition = 12x+2x=14x

On Multiplication = 12x✕2x = 24x²

Now, 3x²+14x+8=0

3x²+12x+2x+8=0

3x(x+4)+2(x+4)=0

(3x+2)(x+4)=0

Now, Take 3x+2=0, x= -2/3 and x+4=0, x=-4

Hence, the values of x are -2/3 and -4.

Type of Quadratic Equations Questions Asked in Bank Exams:

Q1. Solve the Equations given below and Mark Answer given:

I. 3x²+14x+8=0

II. 4y²+16y+7=0

Give Answer:

1. x>y

2. x<y

3. x≥y

4. x≤y

5. x=y or No relationship can be establish between x and y

Explanations:

I. 3x²+14x+8=0

3x²+12x+2x+8=0

3x(x+4)+2(x+4)=0

(3x+2)(x+4)=0

Now, Take 3x+2=0, x= -2/3 and x+4=0, x=-4

Hence, the values of x are -2/3=-0.226 and -4.

II. 4y²+16y+7=0

4y²+14y+2y+7=0

2y(2y+7)+1(2y+7)=0

(2y+1)(2y+7)=0

Now, Take 2y+1=0, y= -1/2 and 2y+7=0, y=-7/2

Hence, the values of y are -1/2=-0.5 and -7/2=-3.5

Now, x=-0.226,-4 and y=-0.5,-3.5

Compare Now,

-0.226>-0.5 it means x>y _____________(1)

-0.226>-3.5 it means x>y ______________(2)

-4<-0.5 it means x<y __________________(3)

-4<-3.5 it means x<y ___________________(4)

> and < never occur together, so we can not establish any relationship between x and y, Hence, Option(5) is correct.

Q2. Solve the Equations given below and Mark Answer given:

I. x²=√196

II. y=√196

Give Answer:

1. x>y

2. x<y

3. x≥y

4. x≤y

5. x=y or No relationship can be establish between x and y

Explanations:

I. x²=√196

x= ±14 means x=+14, -14

II. y=√196

y=14

Compare Now,

+14=+14 it means x=y _____________(1)

-14<+14 it means x<y ______________(2)

On combining, (1) and (2), we get x≤y, Hence Option(4) is the correct answer.

[Note: We take ± sign only when we make square root if square root is already made in any specific sign then we take only the sign in which its given.] 

Tips to Select Answer in Quadratic Comparison Questions in Bank Exams:

x= x₁=First Obtained Value of x, x₂= Second Obtained Value of x

y= y₁=First Obtained Value of y, y₂= Second Obtained Value of y

#01. Comparison Condition when we need to select Answer x>y.

All the four equations must show x>y.

First Obtained Value of x>First Obtained Value of y means x>y _____________(1)

First Obtained Value of x>Second Obtained Value of y means x>y  ___________(2)

Second Obtained Value of x>First Obtained Value of y means x>y ____________(3)

Second Obtained Value of x>Second Obtained Value of y means x>y___________(4)

#02. Comparison Condition when we need to select Answer x<y.

All the four equations must show x<y.

First Obtained Value of x<First Obtained Value of y means x<y _____________(1)

First Obtained Value of x<Second Obtained Value of y means x<y  ___________(2)

Second Obtained Value of x<First Obtained Value of y means x<y ____________(3)

Second Obtained Value of x<Second Obtained Value of y means x<y___________(4)

#03. Comparison Condition when we need to select Answer x=y.

All the four equations must show x=y.

First Obtained Value of x=First Obtained Value of y means x=y _____________(1)

First Obtained Value of x=Second Obtained Value of y means x=y  ___________(2)

Second Obtained Value of x=First Obtained Value of y means x=y ____________(3)

Second Obtained Value of x=Second Obtained Value of y means x=y___________(4)

#04. Comparison Condition when we need to select Answer x≥y.

When at least on of four equations show x=y and rest show x>y or When at least on of four equations show x>y and rest show x=y.

#05. Comparison Condition when we need to select Answer x≤y.

When at least on of four equations show x=y and rest show x<y or When at least on of four equations show x<y and rest show x=y.

#06. Comparison Condition when we need to select Answer "No relationship can be establish between x and y".

When at least on of four equations show x>y and also When at least on of four equations show x<y.