1.2. l1. sol of quadratic eq by factorization

SUBJECT : MATHEMATICS
CLASS : MATRIC
CHAPTER ( 2/4 ) : EQUATIONS
LESSON NO : 01 OF 09
TOPIC : SOLUTION OF
QUADRATIC EQUATION
BY FACTORIZATION
s k y h a w k s 2 f l y / 0 3 3 3 9 3 0 2 2 5 6 s k y h a w k s

Q. What is meant by the solution of an equation?
A. By the solution of an equation we mean to find the
value of variable which satisfies the equation.
Q. What is meant by the degree of an equation?
A. Maximum power of the variable in the equation is
called degree of equation.
Q. What is meant by the quadratic equation?
A. An equation in which maximum power of the
variable is two is called quadratic equation.

Q. How can we solve a quadratic equation?
A. We can solve a quadratic equation by these
methods.
(i) Factorization method
(ii) Completing square method
(iii) Quadratic formula

 Quadratic Equation
 Factorization Method
 Related Examples

Quadratic Equation
 An equation in one variable
 Maximum power of variable is two
Examples
2x2 – 5x + 3 =0
9x2 – 13x + 7 =0
SOLUTION OF QUADRATIC EQUATION
BY FACTORIZATION

General form of quadratic equation is
ax2 + bx + c = 0 ; (a  o)
Where a & b are the coefficients of the second and the
first degree terms respectively, and ‘c’ is constant.
Quadratic Equation
BY FACTORIZATION

Factorization Method
In this method, we factorize the given equation
and get two factors which on equating to zero, give the
required two values for unknown.
BY FACTORIZATION

Solve by factorising: x2 + 7x + 12=0
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
Write down all
the factor pairs
of 12.
From this list,
choose the pair that
adds up to 7
3 + 4 = 7
Put these numbers
into brackets
0 = (x + 3)(x + 4)
x = – 3 and – 4
Multiply constant
term”12” and the term
“x2”
What will be the
answer?
Ans. “12 x2”
Note: Now make
such factors of “7x”
so that their sum
should be equal to
“7x” and product
equal to “12 x2”.
(x +....)(x+….)

Solve by factorising: 0 = x2 + x - 6
1 x -6 = -6
2 x -3 = -6
3 x -2 = -6
6 x -1 = -6
Write down all the
factor pairs of – 6
From this list,
choose the pair
that adds up to 1
(3) + (-2) = 1
3 – 2 = 1
Put these numbers
into brackets
0 = (x + 3)(x - 2)
x = – 3 and 2
Multiply constant
term”-6” and the term
“x2”.
What would be the
answer ?
Ans:- “-6x2 “
Note: Now make
such factors of “x”
so that their sum
should be equal to
“x” and product
equal to “-6x2”.

Copy and fill in the missing
values when you factorise
x2 + 8x + 12 = 0
Find all the factor pairs of 12
1 x 12 = 12
2 x _ = 12
3 x 4 = 12
From these choose the pair
that add up to 8
_ + 6 = 8
Put these values into the
brackets (x + _)(x + _) = 0
x = -2 and - 6

Example 1
Solve x2 - 3x = 2x – 6
BY FACTORIZATION
Solution
x2 - 3x = 2x – 6
x2-5x+6 = 0
x2-3x-2x+6 = 0
x(x-3)-2(x-3) = 0

(x-2) (x-3) = 0
x-2 = 0 or x-3 = 0
x = 2 or x = 3
Solution set = { 2 , 3 }
BY FACTORIZATION

BY FACTORIZATION
Solution
3x2 +4x-4=0
3 x2+6x-2x-4 = 0
3x(x+2)-2(x+2) = 0

(x+2) (3x-2) = 0
x+2 = 0 or 3x-2 = 0
x=-2 or x = 2/3
Solution set = { -2 , 2 / 3 }
BY FACTORIZATION

1. x2 + 5x + 6 = 0
2. x2 - x – 6 = 0
3. x2 + 8x + 12 = 0
4. x2 + x – 12 = 0
5. x2 - 8x + 15 = 0
6. x2 + 3x – 21 = 0
7. x2 - 3x – 18 = 0
8. x2 - 10x – 24 = 0
9. x2 + 8x + 16 = 0
10. x2 - 4x – 60 = 0
(x+…)(x+…)
(x–…)(x+…)
-3 and -2
3 and -2
(x+…)(x+…) -2 and -6
(x–…)(x+…)
(x–…)(x–…)
(x+…)(x–…)
(x–…)(x+…)
(x-…)(x+…)
(x+…)(x+…)
(x-…)(x+…)
3 and -4
3 and 5
-7 and 4
6 and -3
12 and -2
-4 and -4
10 and -4
(x+3)(x+2)
(x–3)(x+2)
(x+2)(x+6)
(x–3)(x+4)
(x–3)(x–5)
(x+7)(x–4)
(x–6)(x+3)
(x-12)(x+2)
(x+4)(x+4)
(x-10)(x+4)
GOOD JOB GUYS!

 Quadratic Equation
 Factorization Method
 Related Examples
SOLUTION OF QUADRATIC EQUATION BY
FACTORIZATION

Q. What is the definition of quadratic equation?
A. An equation in one variable and the maximum
power of variable is two is called Quadratic
Equation.
Q. What is the general form of quadratic equation?
A. General form of quadratic equation is
ax2 + bx + c = 0 ; (a  o)
BY FACTORIZATION

Assignment
Solve the following for ‘x’ by factorization method.
(i) 9x2 –12x – 5 = 0
(ii) x (x+7) = (2x-1) (x+4)
(iii) x 2–x = 2
SOLUTION OF QUADRATIC EQUATION BY
FACTORIZATION

BY
COMPLETING SQUARE METHOD

1.2. l1. sol of quadratic eq by factorization

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