**An equation of the form ax**where a= coefficient of x

^{2}+bx+c=0 is called quadratic equation^{2}, b= coefficient of x and c= constant.

**ax**always have two solutions.

^{2}+bx+c=0**Discriminant Method to find the Value of x:**

x = (-b±√(b^2-4ac))/2a

**Eg- 3x**

^{2}+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:**

ax

^{2}+bx+c=0
acx

^{2}= Multiplication of factor bx which must result bx on addition**Eg- 3x**

^{2}+14x+8=0

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

acx

^{2}=8✕3x^{2}= 24x^{2}
Now see the factor of 14x which gives 24x

^{2}i.e. 12x✕2x
You also need to see that addition of the factor of 14x must result 14x and multiplication mus result 24x

^{2}
Here factor of 14x are 12x and 2x

On addition = 12x+2x=14x

On Multiplication = 12x✕2x = 24x

^{2}
Now, 3x

^{2}+14x+8=0
3x

^{2}+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. 3x**

^{2}+14x+8=0

**II. 4y**

^{2}+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. 3x

^{2}+14x+8=0
3x

^{2}+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. 4y

^{2}+16y+7=0

4y

^{2}+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. x**

^{2}=√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. x

^{2}=√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= x

_{1}=First Obtained Value of x, x_{2}= Second Obtained Value of x
y= y

_{1}=First Obtained Value of y, y_{2}= 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.

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