Question

What is a quartic function with only the two real zeros given?

x = -4 and x = -1

Answer 1

Remark

Now we have to get two more zeros from somewhere. Let us say that the last factor is x^2 + 4 which gives a pair of complex answers. The complete quartic could be something like

y = (x + 4)(x + 1)(x^2 + 4)

The graph follows.