You should be able to
use factorisation to solve quadratic equations
Steps to solving quadratic equations:
1) Must make sure one side of the equation is always equals to zero before you start.
2) Factorise by cross multiplication method.
[Note: Sometimes you may need to take out common factors]
3) Solve by making each bracket equals to zero
Zero Product Principle
Key idea to solving quadratic equations
In general: For A x B = 0, either A = 0 or B = 0.
The idea is to have two factors multiplied together to be equal to zero.
It can look like the following example:
Eg 1: 2p(p -3) = 0,
Eg 2: (x + 1)(x - 3) = 0
To solve we need to let one bracket both brackets be equal to zero
Eg 1: 2p(p - 8) = 0
2p = 0 or (p - 8) = 0
p = 0 or p - 8 = 0
p = 8
Reason:
Ask yourself the following question:
1) What will you multiply to (p - 8) to get zero? You know u need to multiply by zero.
Therefore 2p must be equal to zero. [ ie: 2p = 0]
2) What will you multiply to 2p to get zero? You know u need to multiply by zero.
Therefore (p - 8) must be equal to zero. [ie: (p - 8) = 0]
Eg 2 : (x + 1)(x - 3) = 0
(x + 1) = 0 or (x - 3) = 0
x + 1 = 0 or x - 3 = 0
x = -1 or x = 3
Reason:
Ask yourself the following question:
1) What will you multiply to (x -3) to get zero? You know u need to multiply by zero.
Therefore (x + 1) must be equal to zero. [ ie: (x + 1) = 0]
2) What will you multiply to (x +1) to get zero? You know u need to multiply by zero.
Therefore (x -3) must be equal to zero. [ie: (x -3) = 0]