3.88: Cubic with given roots

0606/22/O/N/24 — Question 3 · 5 marks

Do not use a calculator in this question.

The polynomial pp is defined by p(x)=ax3−3x2−3x+bp(x) = ax^{3} - 3x^{2} - 3x + b, where aa and bb are constants.
(a)
Given that x=2x = 2 and x=−1x = -1 are roots of the equation p(x)=0p(x) = 0, find aa and bb.
[3]
(b)
Solve the equation p(x)=0p(x) = 0.
[2]