Question

three functions in standard form.
One function, f(x), with two real rational solutions.
One function, g(x), with two real irrational solutions.
One function, h(x), with two complex solutions.

Answer 1

for the first one you could try
\[(x-1)(x-3)\] which has to rational solutions, namely \(1\) and\(3\)

Answer 2

of course that is not in standard form, you would have to multiply it out

Answer 3

2 complex solutions is the easiest, you could use \(x^2+1\) say because if you solve \(x^2+1=0\) you get \(x^2=-1\) and therefore \(x=\pm i\)