(a) Show that if the equation ax³ + bx + c = 0 has a repeated root a then 3aα² + b = 0.

(b) A can is to be made in the form of a circular cylinder of radius r (in cm) and height h (in cm), as shown in Figure 2.36. Its capacity is to be 0.5 l. Show that the surface area A (in cm²) of the can is

Using the result of (a), deduce that A has a minimum value A* when 6πr² – A* = 0. Hence find the corresponding values of r and h.

Transcribed Image Text:

A = 2tr + rcm 0.5 litres Figure 2.36 1000 r h cm