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This comes in two parts, with the first being less fiendish than the second. Itâ€™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.

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.

In this activity you will need to work in a group to connect different representations of quadratics.

# Discriminating

##### Age 16 to 18
$$ax^2 + bx + c = 0,$$
where $a$, $b$ and $c$ are allowed to be any real numbers except that $a$ is not $0$.