Question 11

11. [Maximum mark: 6]

A biologist believes that there is a relationship between the possible population size of a group of birds ($p$ thousand) and the population of a colony of wasps ($w$ thousand). Based on her research she believes that the relationship is:

$w = p^3 - 4p^2 + 3p$

(a) When $w = 0$, find the possible values of $p$. [2]

(b) Determine the positive values of $w$ for which there is only one positive value of $p$. [4]