### Discriminating

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

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.

##### Stage: 5

This resource is from Underground Mathematics (previously known as the Cambridge Mathematics Education Project).

(i) Find all real solutions of the equation
$$(x^2−7x+11)^{(x^2−11x+30)}=1.$$

(ii) Find all real solutions of the equation
$$(2−x^2)^{(x^2−3\sqrt{2}x+4)}=1.$$

This is an Underground Mathematics resource.

Underground Mathematics is funded by a grant from the UK Department for Education and provides free web-based resources that support the teaching and learning of post-16 mathematics. It started in 2012 as the Cambridge Mathematics Education Project (CMEP).

Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.