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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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Equations
Page 2

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
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.
(    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
Page 3

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
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.
(    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
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

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
In word problem, the solution thus obtained should always be
checked with conditions given in the question.
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
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## Mathematics (Maths) Class 10

59 videos|362 docs|103 tests

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