Question

How can one determine the zeros of a function? 

Answer 1

They are the values of 'x' that make the function zero.

If you graph the function, they are the values of 'x' where the graph
crosses the x-axis.

Answer 2

$the\ argument\ x\, for\ which\ the\ value\ y\ of\ the\ function\ is\ zero\\\\e.g.\\y=2x-6\ \ \ \Rightarrow\ \ \ the\ zeros\ of\ a\ function\ is\ x=3\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (y=2\cdot3-6=6-6=0)\\\\y=x^2+8x\ \ \ \Rightarrow\ \ \ the\ zeros\ of\ a\ function\ are\ x=0\ \ \ or\ \ \ x=-8\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (y_1=0^2+8\cdot0=0;\ y_2=(-8)^2+8\cdot(-8)=64-64)$