My professor assigned this exercise and I'm not really sure how to get it started.

Suppose $\displaystyle f(a,b)<0$ and $\displaystyle f(c,d)>0$. Let $\displaystyle \phi : [0,1]\rightarrow R^2$ be determined by $\displaystyle \phi (t)=(1-t)(a,b)+t(c,d)$. Apply Bolzano's Intermediate Value Theorem to $\displaystyle g=f(\phi )$.

Any guidance would be appreciated.