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.
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