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Title : How To Solve Quadratic Equations For Banking Concern Po | Know Here
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How To Solve Quadratic Equations For Banking Concern Po | Know Here

An equation of the cast ax²+bx+c=0 is called quadratic equation where a= coefficient of x², b= coefficient of x as well as c= constant. A Quadratic Equation ax²+bx+c=0  always arrive at got 2 solutions.

Discriminant Method to respect 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 respect the value of x:

ax²+bx+c=0 

acx² = Multiplication of component subdivision bx which must lawsuit bx on addition

Eg- 3x²+14x+8=0

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

acx²=8✕3x² = 24x²

Now come across the component subdivision of 14x which gives 24x² i.e. 12x✕2x

You too involve to come across that improver of the component subdivision of 14x must lawsuit 14x as well as multiplication mus result 24x²

Here component subdivision of 14x are 12x as well as 2x

On improver = 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 as well as x+4=0, x=-4

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

Type of Quadratic Equations Questions Asked inwards Bank Exams:

Q1. Solve the Equations given below as well as 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 human relationship tin endure constitute betwixt x as well as 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 as well as x+4=0, x=-4

Hence, the values of x are -2/3=-0.226 as well as -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 as well as 2y+7=0, y=-7/2

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

Now, x=-0.226,-4 as well as y=-0.5,-3.5

Compare Now,

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

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

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

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

> as well as < never hap together, thence nosotros tin non constitute whatever human relationship betwixt x as well as y, Hence, Option(5) is correct.

Q2. Solve the Equations given below as well as 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 human relationship tin endure constitute betwixt x as well as y

Explanations:

I. x²=√196

x= ±14 way x=+14, -14

II. y=√196

y=14

Compare Now,

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

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

On combining, (1) as well as (2), nosotros get x≤y, Hence Option(4) is the right answer.

[Note: We arrive at got ± sign exclusively when nosotros brand foursquare root if foursquare root is already made inwards whatever specific sign as well as then nosotros arrive at got exclusively the sign inwards which its given.] 

Tips to Select Answer inwards Quadratic Comparison Questions inwards 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 nosotros involve to choose Answer x>y.

All the iv equations must exhibit 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 nosotros involve to choose Answer x<y.

All the iv equations must exhibit 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 nosotros involve to choose Answer x=y.

All the iv equations must exhibit 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 nosotros involve to choose Answer x≥y.

When at to the lowest degree on of iv equations exhibit x=y as well as residual exhibit x>y or When at to the lowest degree on of iv equations exhibit x>y as well as residual exhibit x=y.

#05. Comparison Condition when nosotros involve to choose Answer x≤y.

When at to the lowest degree on of iv equations exhibit x=y as well as residual exhibit x<y or When at to the lowest degree on of iv equations exhibit x<y as well as residual exhibit x=y.

#06. Comparison Condition when nosotros involve to choose Answer "No human relationship tin endure constitute betwixt x as well as y".

When at to the lowest degree on of iv equations exhibit x>y as well as too When at to the lowest degree on of iv equations exhibit x<y.

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