A LevelMaths: Pure 1CIERevision Notes1. Algebra & Functions1.1 Quadratics1.1.3 Discriminants

Discriminants (CIE A Level Maths: Pure 1)

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Discriminants

What is a discriminant?

  • The discriminant is the part of the quadratic formula that is under the square root sign b squared minus 4 a c
  • It is sometimes denoted by the Greek letter capital delta (capital delta) 

How does the discriminant affect graphs and roots?

There are three options for the outcome of the discriminant:

  • If b squared minus 4 a c space greater than 0 the quadratic crosses the x-axis twice meaning there are two distinct real roots
  • If  b squared minus 4 a c equals 0 the quadratic touches the x-axis once meaning there is one real root (also called repeated roots)
  • If  b squared minus 4 a c space less than 0 the quadratic does not cross the x-axis meaning there are no real roots

Discrimamts Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes

Discriminant and inequalities

  • You need to be able to set up and solve equations and inequalities (often quadratic) arising from the discriminant
  • Sketch the quadratic and decide whether you're looking above or below zero to write your solutions correctly

 Discrimamts Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes 

Examiner Tip

  • When questions just mention “real roots”, the roots could be distinct or repeated (i.e. they arent talking about complex numbers!)
  • In these cases, you only need to worry about solving b squared minus 4 a c greater or equal than 0
  • When solving using inequalities always sketch the quadratic and decide whether you're looking above or below zero to help write your solutions correctly

Worked example

Discriminants Example Diagram, A Level & AS Level Pure Maths Revision Notes

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    Paul

    Author: Paul

    Expertise: Maths

    Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.