Question

Determine an expression for f(x) in which:

f(x) is a cubic function,
has two roots,
f(x) >= 0 when x <= 2, f(x)<0 when x>2

Answer 1

A cubic must have a total of 3 roots, both real and imaginary
Every cubic MUST have at least 1 real root and
complex roots always come in pairs.
So we have :
1 real root, 2 complex or
3 reals

So to have 2 complex only is not possible
I can see 2 equal real roots and one other real .

how about
f(x) = -x^2(x-2)

check it by running it trough a graphing page like
www.desmos.com/calculator