2.13: Repeated positive integer root

0606/23/O/N/17 — Question 11 · 8 marks

The cubic equation x3+ax2+bx36=0x^{3} + ax^{2} + bx - 36 = 0 has a repeated positive integer root.
(i)
If the repeated root is x=3x = 3 find the other positive root and the value of aa and of bb.
[4]
(ii)
There are other possible values of aa and bb for which the cubic equation has a repeated positive integer root. In each case state all three integer roots of the equation.
[4]