Solving Quadratic Equations (Edexcel IAL Maths)

Spec point — 1.5

Solving quadratic equations

• We can solve quadratic equations when they are written in the form $ax^{2}+bx+c=0$

• If given an unusual looking equation, try to rearrange it into this form first

• The three ways to solve a quadratic you must know are

  • Factorising
  • Completing the square
  • Quadratic formula

How do I solve by factorisation?

• Factorising is a great way to solve a quadratic quickly but won't work for all quadratics
• If the numbers are simple, try factorising first
• Once factorised, set each bracket to = 0 and solve

How do I solve by completing the square?

• Completing the square will work for any quadratic
• Make sure you know how to complete the square
• Remember this will help with questions involving turning points too

How do I solve using the quadratic formula?

• The quadratic formula might look complicated but it just uses the coefficients a, b and c from the quadratic equation
• The quadratic formula will work for any quadratic

How do I solve using a calculator?

• Most calculators now have the ability to solve quadratics
• Get used to how your calculator functions work
• So the solution to the quadratic equation $2x^{2}+5x-12=0$ are x = 1.5 and x = -4

Exam Hint

• A calculator can be super-efficient but be aware some marks are for method

• There will never be many marks for solving a quadratic at AS/A level

• Use your judgement:

  • is it a “show that” or “prove” question?
  • how many marks?
  • how long is the question?

• Remember the quadratic formula with a song... there are loads of fun ones on YouTube

Worked Example