Quadratic Equations Summary

1. Block 2
Solving Quadratic Equations
Summary

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

3. 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

4. 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)
53– ++ –
+ 3 – 5
x + 3 = 0 or x – 5 = 0
solutions x = -3 or x = 5

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

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

7. Solve 3x2
– 8x + 2 = 0
-b +
– √ b2
– 4ac
2a
x =
ax2
+ bx + c = 0
a = 3 b = -8 c = 2
8 +
– √ 82
– 4(3)(2)
2(3)
8 +
– √ 40
6
8 +√ 40
6
8 – √ 40
6
OR
Beware when
using calculator
= 2.39 or = 0.28

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

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

10. Completing Square method
x2
– 6x + 5 = 0
(x – 3)2
– 9 + 5 = 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