Solving quadratic equations by factorising

To solve a quadratic equation, the first step is to write it in the form: ax² + bx + c = 0. 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 x² - 9x + 20 = 0

Solution

• First, factorise the quadratic equation x²- 9x + 20 = 0

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

  (x - 4) (x - 5) = 0

• 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 substitutuing 4 and 5 in to the equation:

  x²- 9x + 20

• Substituting 4 gives:
• 4² - 9 × 4 + 20 = 16 - 36 + 20 = 0
• Substituting 5 gives:
• 5² - 9 × 5 + 20 = 25 - 45 + 20 = 0

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

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