Show that the equation \[x^3+3x^2 - 3 = 0\] has one positive root.

‘Every cubic has at least one real root.’ True or false?

Can we show we have a positive root here?

Can we show we have only one?

Find to three decimal places an approximation to this root.

There is more than one way of doing this…

In 1952, when this question was first set, students did not have calculators, so more efficient methods were preferable!