solving quadratic equation using
1. Using Factorization Method
2. Using Formula Method
3. Using Completing the Square Method
STEPS ON HOW TO SOLVE QUADRATIC EQUATION BY
FACTORIZATION METHOD
Example: x2
+ 5x – 6 = 0
Step 1: Firstly note
the coefficient of x2
Coefficient
= 1
Step 2: Find the product
(the
multiplication
of the coefficient of x2 and the constant)
Product
= 1 x - 6
Step 3: Note the sum
Sum
= +5
Step 4: Then find the
factors (two
numbers multiplied together to give the product; -6 and when
Summed gives the Sum; +5)
Factors
= 6 and -1
Step 5: Write the
equation, replacing the sum with the factors
x2
+ 6x – x – 6
Step 6: Group them into
two
(
x2 + 6x) – (x – 6)
Step 7: Find the common
factors of each expression in the bracket
Common
factors = x and -1 respectively.
Step 8: Put the common factors
outside the bracket of their respective expression
x
(x + 6) – 1 (x + 6)
Note:
(Be careful of the
signs here and also note this
whenever you find out that the two numbers inside the bracket are not the same
then you are not correct and you need to start all over again)
Step 9: Pick one of the
expressions in the bracket (since both of them in the bracket are the
same) and the ones outside the
bracket.
Note: Be careful of
the signs at this stage
(x
+ 6) (x – 1)
Step 10: Equate the
expressions to zero
(x
+ 6) (x – 1) = 0
Step 11: Then equate
each of the expression to zero
x+
6 = 0 or x – 1 = 0
Step 12: Take the
constant to the other side across the equal sign (=)
Note: Performing this
task the sign changes
x
= -6 or x = 1
Step 13: Make x the
subject of the formulae (by dividing both sides with the coefficient of x at
that moment)
x
= 6 or x
= 1
1 1
1 1
Step 14: Express the root
as x, x1
-6,
1 (ANSWER)
STEPS ON HOW TO SOLVE QUADRATIC EQUATION BY FORMULA METHOD
Example: 2x2
+ 3x – 5 = 0
Step 1: Write down the
formula
-b+-√b2 – 4ac
2a
Step 2: Write down the values
of the alphabet indicated in the formula from the equation. i.e.
(a = coefficient of x2, b
= coefficient of x and c = constant)
a = 2, b = 3 and c = -5
Step 3: Replace the
alphabet with the values respectively
Note: Be careful of
the signs as they change
-3+-√32 – 4 x 2 x -5
2 x 2
Step 4: Evaluate it (Be careful of
signs)
-3+-√9 + 40
4
-3+-√49
4
-3+-7
4
Step 5: Split the
evaluated value into two, (one carries the positive sign, while the other carries the
negative sign)
-3 + 7 or -3 -
7
4 4
Step 6: Evaluate each
of the expression (Be careful of the signs)
4 or -10
4 4
Step 7: Divide to the
minimum
1 or -5
Step 8: Write the roots
as x, x1
1, -5 (ANSWER)
2
STEPS ON HOW TO SOLVE QUADRATIC EQUATION BY COMPLETING THE
SQUARE METHOD
Example: 2x2 + 5x +3 = 0
Step 1: Divide
through by the coefficient of x2 i.e.
(2)
2x2 + 5x+
3 = 0
2
2 2 2
Step 2: Evaluate
it
x2
+ 5x + 3 = 0
2 2
Step 3: Take the
constant across the equal (=) sign
Note: The sign changes
x2 + 5x = -3
2 2
Step 4: From the
left side (Multiply it by half, take off the square from the x2 and put it
outside
the
bracket and subtract the square from it)
(x
+ 5) 2 x 1 – 5
2 = -3
2 2 4
2
Step 5: Evaluate
it
(x + 5 ) 2 – 25 = -3
4 16
2
Step 6: Try
making x the subject by taking all constants to the other side
(x + 5) 2 =
-3 + 25
4
2 16
Step 7: Evaluate
the right side (the denominator is 16)
(x
+ 5) 2 = -24 + 25
4
16
(x
+ 5 ) 2 = 1
4
16
Step 8: Take the
square of both sides
√x + 5 2 =
√1
4 16
x
+ 5 = +-1
4 4
Step 9: Make x
the subject of the formula
4 4
Step 10: Evaluate
it
x
= -5 +-1
4
Step 11: Split the
evaluated value into two, (one carries the positive sign, while the other carries
the
negative sign)
x
= -5 + 1 or x = -5- 1
4
4
Step 12: Evaluate
it
x
= -4 or x = -6
4
4
x = - 1 or x =
- 3
Step 13: Write the
roots as x, x1
1, -3 (ANSWER)
STEPS IN SOLVING DECIMAL PLACES (ROUNDING OFF)
Example: 34. 8259
Before
you start, you must take this to consideration; that the figures before the
full stop (.) must be kept constant and not to be altered and only when the
figure to be rounded up is up to 5 but less than 10 before you can approximate
it. We can either round off to 1 d.p, 2 d.p, 3 d.p, 4 d.p etc depending the
question being asked.
I
will like us to round off the above example to 1 d.p, 2 d.p and 3 d.ps
To 1 decimal
place
Step 1: Number the
figures after the fall stop (.) starting from 1 till the end of the figures. (Invisible
numbering)
34. 8 2 5 9
1 2 3 4
1 2 3 4
Step 2: note where 1 is
which is at 8. Then you approximate the figure immediately after to become 1
and add it to the figure preceding it. (since the figure immediately after it is not up to
5 or less than 10, I will round it up to become zero and then add it to the one
preceding it)
34. 8 (Ans)
To 2 decimal
place
Step
1: following step 1 of (a) then round off the figure immediately after it to
become 1 and then add it to the one preceding it.
34. 8 3 (Ans)
To 3 decimal
place
Step
1: following step 1 of (a) then round off the figure immediately after it to
become 1 and then add it to the one preceding it.
34. 8 2 6 (Ans)
STEPS IN SOLVING SIMPLE EQUATIONS
Example: 3x – 3
= 5x + 9
Step 1: find the
figures with common features
3x and 5x has common features, which
is x
-3 and +9 has common features, which
is constant
Step 2: collect like
terms (the figures with common features should be separated from the other)
Note: Once a number crosses the (=) equal sign, the sign of that
number changes. (+ becomes – while – becomes +)
3x – 5x = 9 + 3
Step 3: Evaluate the
expression
-2x = 12
Step 4: make x the
subject of the formulae by dividing through by the coefficient of x, which is
-2
-2x = 12
-2 -2
X= -6
Ans: - 6 simple equations
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