Solving quadratic equations by factorising

To solve a quadratic equation, the first step is to write it in the form:

Then factorise the equation as you have revised in the previous section.

If we have two numbers, A and B, and we know that A × B = 0, then it must follow that either A = 0, or B = 0 (or both). When we multiply any number by 0, we get 0.

Example

Solve the equation:

Solution

• First, factorise the quadratic equation

  

• Find two numbers which add up to 9 and multiply to give 20. These numbers are 4 and 5.

  

• Now find the value x so that when these brackets are multiplied together the answer is 0.

  This means either (x - 4) = 0 or (x - 5) = 0

  So x = 4 or x = 5.

• You can check these answers by substituting 4 and 5 in to the equation:

  

• Substituting 4 gives:

• 

• Substituting 5 gives:

• 

Remember these 3 simple steps and you will be able to solve quadratic equations.

Now try a Test Bite