1.12: Cubic Roots and a Parameter

4PM1/2R/June/2019 — Question 1 · 7 marks

f(x)=(x3)[x2+(p2)x+q].f(x)=(x-3)\left[x^2+(p-2)x+q\right].
Given that f(0)=12\displaystyle f(0)=-12,
(a) find the value of q\displaystyle q.
(2)
(b) Find the range of values of p\displaystyle p for which the cubic equation f(x)=0\displaystyle f(x)=0 has only one real root.
(5)