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Powerful Quadratics

This comes in two parts, with the first being less fiendish than the second. It’s great for practising both quadratics and laws of indices, and you can get a lot from making sure that you find all the solutions. For a real challenge (requiring a bit more knowledge), you could consider finding the complex solutions.

Discriminating

You're invited to decide whether statements about the number of solutions of a quadratic equation are always, sometimes or never true.

Factorisable Quadratics

This will encourage you to think about whether all quadratics can be factorised and to develop a better understanding of the effect that changing the coefficients has on the factorised form.

Submit A Solution

We love receiving your thoughts about and solutions to our live problems. We review and edit these for the benefit of other students. To see the most recently solved problems go to the primary student or secondary student solution pages.


What we like to see

We have written an article on what we are looking for when we decide which solutions to publish.

Explain your methods clearly for other school students to read.
Give reasons and convincing arguments or proofs where you can.

You can share your work with us by typing into the form or uploading a file (must be less than 10MB.)

What can I upload?

  • Word documents
  • PDF files
  • Images - any format
  • Screenshots
  • Photos of written work

You can also send us URLs to your work on:

  • Youtube/Vimeo
  • Google Docs
  • Sharepoint/Office 365
  • Anywhere sensible on the internet!

How we use your information

By uploading your solution here you are giving us permission to publish your work, either as a whole or edited extracts, on the NRICH website and in associated educational materials for students and teachers, at our discretion.

For our full terms of use regarding submitted solutions and user contributions please see https://nrich.maths.org/terms

Your information (first name, school name etc) is optional. If supplied, it may be used for attribution purposes only if your work is published on the website. Data that you supply on this form (e.g. age if supplied, location if supplied) may also be anonymised and used for evaluation and reporting.

For more information about the University's policies and procedures on handling personal information, and your rights under data protection legislation, please see https://www.information-compliance.admin.cam.ac.uk/data-protection/general-data.