Originally Posted by

**zebra2147** I could really use some help. Not really sure how to get started.

Suppose $\displaystyle f(a,b)< 0$ and $\displaystyle f(c,d)>0$. Construct nested intervals $\displaystyle [a_{n},b_{n}]$ and $\displaystyle [c_{n},d_{n}]$ such that $\displaystyle f(a_{n},c_{n})\leq 0$ and $\displaystyle f(b_{n},d_{n})>0$. Then show $\displaystyle f(x_{0},y_{0})=0$ if $\displaystyle \bigcap _{n=1}^\infty [a_{n},b_{n}]=\{x_{0}\}$ and $\displaystyle \bigcap _{n=1}^\infty [c_{n},d_{n}]=\{y_{0}\}$.