Quadratic Equation Methods | Mathematics for GCSE/IGCSE - Year 11 PDF Download

When to Solve by Factorisation

• Factorisation is used when the question specifically asks to solve by factorisation. 
• For example:
  • Part (a): Factorise 6x² - 7x - 3
  • Part (b): Solve 6x² - 7x - 3 = 0
• Factorisation is also employed when dealing with two-term quadratic equations. 
• For instance:
  • Solving x² - 4x = 0 by taking out a common factor of x to obtain x(x - 4) = 0, resulting in x = 0 and x = 4
  • Solving x² - 9 = 0 by using the difference of two squares to factorise it as (x + 3)(x - 3) = 0, giving x = -3 and x = 3 (Alternatively, rearranging to x² = 9 and using ±√  to get x = ±3)

When should I use the quadratic formula?

• When solving for equations that require solutions accurate to a given precision such as 2 decimal places or 3 significant figures.
• When the quadratic formula proves to be a faster method compared to factorization. 
  • For instance, when dealing with equations like 36x² - 33x - 20 = 0.
• If uncertain about which method to use, resorting to the quadratic formula is a reliable approach as it always provides solutions.

When should I solve by 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
• When making x the subject of harder formulae containing 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: