Solving Quadratic Equations

1
Solving Quadratic EquationsIn Fraction Form
Remember Our Golden Rule
But first, lets look at LINEAR equations in
Fraction Form
Some Revision from earlier lessons..
2
MULTIPLY by the LCD of the bottom line.
5
2
2
(The LCD is 10)
(Its all on ONE LINE)
Now its in the correct form. Similarly for
Quadratic Equations
3
Solving Quadratic EquationsIn Fraction Form
The LCD is x, since it is the only term on the
bottom line
(Multiply across by x)
1
Get rid of brackets
On ONE line
4
Solving Quadratic EquationsIn Fraction Form
-
Its in the correct form
But can we FACTORISE ?
Guide number 3 1x3
Subtract to 2 Yes! Perfect
Factorised
Solved
Correct!
5
Factors OR -b Formula Look for the Clue
If it says to 1 or 2 decimal places I MUST use
the b formula
Yes. Yes. Yes. I prefer factors.
If it just says Solve I can choose?
6
Solving Quadratic EquationsIn Fraction Form
The LCD is 2x-3, since it is the only term on the
bottom line.
(Multiply by 2x-3)
1
Get rid of brackets
All on ONE line
Tidy UP
divide by 4 .
7
Solving Quadratic EquationsIn Fraction Form
No need for the b formula? Why?
We can FACTORISE

Guide number 4 1x4 2x2
Sum to 5 No Good
Sum to 4 PERFECT
Factorised
Solved
Two Equal Roots
Correct!
8
Solving Quadratic EquationsIn Fraction Form
The LCD is x(x1). We will be able to divide this
LCD by both x and x1.
BRAIN TEASER
Whats wrong with using x1 as the LCD???
Same thing thats wrong with dividing the 10 on
top by the 10 on the bottom.
9
Solving Quadratic EquationsIn Fraction Form
The LCD is x(x1).
Multiply by x(x1)
(1)
(1)
Get rid of the bottom line
All on ONE line
Tidy UP
10
Solving Quadratic Equations .
-
Subtract to 83 No Good
Can we FACTORISE ?
Guide number 84 1x84 2x42 3x28 4x21 6x14 7x12
Subtract to 40 No Good
Subtract to 25 No Good
YES we can
Subtract to 17 Perfect!
Group together
Factorised
Solved
11
The b FORMULAWHAT YOU MUST KNOW
Golden Rule
x equals minus b plus or minus the square root
of b squared minus 4ac all over 2a
You MUST use the b formula when asked to give
the solutions
correct to 1 or 2 decimal places
OR
in SURD form
Why do you need the b formula for the next one.
12
Solving Quadratic EquationsIn Fraction Form
The LCD is x(x-1). We will be able to divide this
LCD by both x-1 and x.
So why do we need to use the b formula?
The code is there.
13
Solving Quadratic EquationsIn Fraction Form
The LCD is x(x-1).
Multiply by x(x-1)
(1)
(1)
Get rid of the bottom line
All on ONE line
Get rid of the brackets
Multiply both sides by -1
14
Solving Quadratic EquationsIn Fraction Form
So
15
Solving Quadratic EquationsIn Fraction Form
GOLDEN RULES
Get everything on ONE line
Get Your Quadratic Equation in the form