Deciding the Quadratic Method (Edexcel IGCSE Maths A (Modular))

Deciding the Quadratic Method

If you have to solve a quadratic equation but are not told which method to use, here is a guide for what to do.

When should I solve by factorisation?

• Use factorisation when the question asks to solve by factorisation

  • For example

    • part (a) Factorise 6x² + 7x – 3

    • part (b) Solve  6x² + 7x – 3 = 0

• Use factorisation when solving two-term quadratic equations

  • For example, solve x² – 4x = 0

    • Take out a common factor of x to get x(x – 4) = 0

    • So x = 0 and x = 4

  • For example, solve x² – 9 = 0

    • Use the difference of two squares to factorise it as (x + 3)(x – 3) = 0

    • So x = -3 and x = 3

    • (Or rearrange to x² = 9 and use ±√ to get x = ±3)

• Factorising can often be the quickest way to solve a quadratic equation

When should I use the quadratic formula?

• Use the quadratic formula when the question says to leave solutions correct to a given accuracy (2 decimal places, 3 significant figures etc)

  • This is a hint that the equation will not factorise

• Use the quadratic formula when it may be faster than factorising
  

  • It's quicker to solve 36x² + 33x – 20 = 0 using the quadratic formula than by factorisation

• Use the quadratic formula if in doubt, as it always works

When should I solve by completing the square?

• Use completing the square when part (a) of a question says to complete the square and part (b) says to use part (a) to solve the equation

• Use completing the square when making x the subject of harder formulae containing both x² and x terms

  • For example, make x the subject of the formula x² + 6x = y

    • Complete the square: (x + 3)² – 9 = y

    • Add 9 to both sides: (x + 3)² = y + 9

    • Take square roots and use ±: 

    • Subtract 3: 

• Completing the square always works

  • But it's not always quick or easy to do