1. Solving Quadratic Equations
The Theory
If one side = 0
Then if a X b = 0
a= 0 or b = 0
We use this to solve quadratic Equations

2. We must first factorise
x2 – 5x = 0
Common Factor
x(x – 5) = 0
Using Theory
x = 0 or
Solutions x = 0 or
x – 5 = 0
x = 5
also known as roots

3. If there is no common factor must be
difference of 2 squares
or trinomial
x2 – 2x – 15 = 0
Trinomial
(x )(x ) = 0
(2 thingies)
(3 thingies) – 3 + – 5 +
+ 3
– 5
or x – 5 = 0
x + 3 = 0
solutions x = -3
or x = 5

4. Sometimes it is difficult to factorise. Sometimes it is impossible!
Luckily we have a formula to solve any quadratic equation.
However!!!!!!!!!

5. The Quadratic Formula To Solve Equation ax2 + bx + c = 0 x = + -b √
b2 – 4ac – 2a
Not on Formula Sheet

6. Solve 3x2 – 8x + 2 = 0
ax2 + bx + c = 0 + -b
a = 3
b = -8
c = 2
x = √
b2 – 4ac – 2a + 8 √
82 – 4X3X2 –
2X3
Beware when using calculator + 8 √ 40 – 6 8 + √ 40 8 – OR √ 40 6 6
= 2.39
or =

7. Sometimes quadratic equations are disguised
x2 - 3x + 4 = 0

8. O x (x + 5) = - 10 Quadratic? No x2 However, breaking brackets
Quadratic Equation
Must make equal to zero
x2 + 5x + 10 =
Now factorise or
Quadratic Formula
No x2 O

9. Completing Square method
x2 – 6x + 5 = 0
(x – 3)2 – = 0
(x – 3)2 – 4 = 0
(x – 3)2 = 4
(x – 3) = √4
x – 3 = 2
x = 5
or x – 3 = -2
or x = 1