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Solving Quadratic Equations (CIE A Level Maths: Pure 1)
Revision Note
Solving Quadratic Equations
Solving quadratic equations
- We can solve quadratic equations when they are written in the form
- 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
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- Factorising
- Completing the square
- Quadratic formula
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Solving a quadratic equation by factorising
- 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
Solving a quadratic equation 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
Solving a quadratic equation by 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
Solving a quadratic equation by 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 are x = 1.5 and x = -4
Examiner Tip
- 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
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