Students will be able to solving quadratic equations algebraically use variety methods (Factorising, Completing Square, and General Formula)
The study of algebra is vital for many areas of mathematics. We need it to manipulate equations, solve problems from unknown variables, and also to develop higher level mathematical theories.
A QUADRATIC EQUATION is an equation which can be written in the form ax2 + bx + c = 0 where a, b, and c are constants and a is not equal to zero.
A quadratic equation may have two, one or zero real solutions.
SOLUTION BY FACTORISATION
For quadratic equations which are not of the form x2 = k, we need an alternative method of solution. One method is to FACTORISE the quadratic and then apply the NULL FACTOR LAW.
The Null Factor Law states that :
When the product of two or more numbers is zero, then at least one of them must be zero.
so if ab = 0 then a = 0 or b = 0
To solve quadratic equations by factorisation, we follow these steps:
Step 1 : If necessary, rearrange the equation so one side is ZERO
Step 2 : Fully Factorise the other side (usually the LHS/Left Hand Side)
Step 3 : Apply the Null Factor Law
Step 4 : Solve the resulting linear equations
|Solution by Factorisation|
COMPLETING THE SQUARE
Some quadratic equations, such as x^2+4x-7=0, cannot be solved using the factorisation methods already practised. This is because the solutions are irrational.
Instead, we use a method called completing the square.
|Completing the Square|
THE QUADRATIC FORMULA
Many quadratic equations cannot be solved easily by factorisation, and completing the square is rather tedious. Consequently, the quadratic formula has been developed.