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# Powerful Quadratics

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### Discriminating

### Factorisable Quadratics

### Which Quadratic?

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Age 16 to 18

- Problem
- Getting Started
- Student Solutions

Find all real solutions of the equation

$$(x^2âˆ’7x+11)^{(x2âˆ’11x+30)}=1.$$

If you were told that two numbers satisfied $a^b=1$, could you write down the possible numbers that a and b could be?

Can you apply the same logic to this question? You might have to think hard to find all the solutions to the given equation. There are more than three solutions”¦

**This is an Underground Mathematics resource.**

$$(x^2âˆ’7x+11)^{(x2âˆ’11x+30)}=1.$$

If you were told that two numbers satisfied $a^b=1$, could you write down the possible numbers that a and b could be?

Can you apply the same logic to this question? You might have to think hard to find all the solutions to the given equation. There are more than three solutions”¦

You're invited to decide whether statements about the number of solutions of a quadratic equation are 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.