# Question of the Week 10: Solving Quadratic Equations

I have found the topic of solving quadratic equations to be a bit of a funny one with students. In my experience, students are not too bad when presented with a quadratic expression and told to factorise it. However, when they are given a factorisable (pretty sure that's a word, if not it should be) quadratic as part of an equation, even when it is already nicely equal to zero, it can go horribly wrong, with mathematical laws broken left, right and centre.

The question above is designed to dig a bit deeper into the minds of students. Here is my thinking behind the choice of answers:

Students go into "solving equations mode" and try to get the x on its own on the left-hand side. Mathematically, of course, there is nothing wrong with this, and students should be encouraged to continue to see where it gets them.

Although this answer looks a bit weird, it is quite a common one in my experience, and it often occurs after students have dabbled fruitlessly with the situation left by starting with option A for a while. They may divide though by x correctly at first, but not liking the look of the nasty fraction, conveniently decide to forget to divide the 40 by x to leave a lovely looking linear equation.