Discriminants (OCR A Level Maths A) : Revision Note

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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 Tips and Tricks

  • 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 Content Creator (Previous)

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.

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