I get really annoyed when questions ask you to sketch stuff, like am doing maths and i'm supposed to be able to do art!

Anyway, I'm not sure on this question:

By sketching the graph of $\displaystyle y = f(x)$ show that

$\displaystyle f(z) \equiv z^4 + 4z + 1 = 0 $

has two negative real roots and no postitive real roots. Show also that $\displaystyle f(z)=0$ has no purely imaginary roots.

Using the argument principle, determine in which quadrants of the complex plane the two complex roots lie.