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# Points to Remember: Quadratic Equations Class 10 Notes | EduRev

## Class 10 : Points to Remember: Quadratic Equations Class 10 Notes | EduRev

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Quadratic
Equations
Page 2

Quadratic
Equations
Quadratic Equations
Factorization Method
Completing The Square
Method
An equation of the form ax
2
+ bx + c = 0, where a, b & c are real numbers & a = 0 is known as a Quadratic Equation
A Polynomial of degree 2 is known as a Quadratic Polynomial
Quadratic Formula
Method
ax
2
+ bx + c = 0 ax
2
+ bx + c = 0 ax
2
+ bx + c = 0
Multiply a & c
a x c = h
Find two numbers
whose product is h and sum is b
These two numbers
can be a and b or any other (p, q)
Split the middle term
accordingly &  take out the
common factors
Finally we’ll get a
product of two linear equations &
hence we can get two values of x
i.e. roots of the equation
Divide the entire equation
by a
Take the constant c / a
on R. H. S.
Now add
(    x coecient of x)
2
on both the sides (L.H.S. & R.H.S.)
So L.H.S. can be written as
where b is the
coecient of x
Now take square root on
both the sides & then simplify the
linear equation to get roots of x
Step 1 :
Step 2 :
Step 3 :
Step 4 :
Step 5 :
Step 1 :
Step 2 :
Step 4 :
Step 3 :
Step 5 :
1
2
Simply take a, b & c
with their respective sign
Find
the two roots of the equation
or
Step 1 :
Step 2 :
Step 3 :
-b ±   b
2
- 4ac
x =
2a
-b +   b
2
- 4ac
x =
2a
-b -    b
2
- 4ac
x =
2a
)
2
(x +
b
2a
QUADRATIC EQUATIONS 10
Page 3

Quadratic
Equations
Quadratic Equations
Factorization Method
Completing The Square
Method
An equation of the form ax
2
+ bx + c = 0, where a, b & c are real numbers & a = 0 is known as a Quadratic Equation
A Polynomial of degree 2 is known as a Quadratic Polynomial
Quadratic Formula
Method
ax
2
+ bx + c = 0 ax
2
+ bx + c = 0 ax
2
+ bx + c = 0
Multiply a & c
a x c = h
Find two numbers
whose product is h and sum is b
These two numbers
can be a and b or any other (p, q)
Split the middle term
accordingly &  take out the
common factors
Finally we’ll get a
product of two linear equations &
hence we can get two values of x
i.e. roots of the equation
Divide the entire equation
by a
Take the constant c / a
on R. H. S.
Now add
(    x coecient of x)
2
on both the sides (L.H.S. & R.H.S.)
So L.H.S. can be written as
where b is the
coecient of x
Now take square root on
both the sides & then simplify the
linear equation to get roots of x
Step 1 :
Step 2 :
Step 3 :
Step 4 :
Step 5 :
Step 1 :
Step 2 :
Step 4 :
Step 3 :
Step 5 :
1
2
Simply take a, b & c
with their respective sign
Find
the two roots of the equation
or
Step 1 :
Step 2 :
Step 3 :
-b ±   b
2
- 4ac
x =
2a
-b +   b
2
- 4ac
x =
2a
-b -    b
2
- 4ac
x =
2a
)
2
(x +
b
2a
QUADRATIC EQUATIONS 10
Nature of Roots: D = b
2
- 4ac
D iscriminant is known for discriminating real and non-real roots as well as
to dene nature of roots.
Conditions:
When  D = 0, roots are real & equal
When  D > 0, roots are real & unequal
When  D < 0, roots are non-real & unequal

Introduction of Quadratic equation
and Factorization method
Scan the QR Codes to watch our free videos
Quadratic formula is derived from completing the square
method
In word questions, try to nd words like product, area,
Pythagoras theorem, etc; where we will multiply two terms
to obtain a quadratic equation.
In word problem, the solution thus obtained should always be
checked with conditions given in the question.
PLEASE KEEP IN MIND
Speed =      , please remember this formula.
A variety of questions on quadratic equations are based on the
concept of speed.  Also do remember conversions like
1 hour = 60 minutes, 1 minute = 60 seconds.
?
To determine whether an equation is quadratic or not, expand
the given equation,  simplify it as much as possible and then check
the highest degree.
?
?
?
?
Distance
Time
QUADRATIC EQUATIONS 11
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## Mathematics (Maths) Class 10

59 videos|362 docs|103 tests

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