Question

By completing the square show that f(x)=0 has only 1 root

F(x)=x^3-2x^2-16

Answer 1

We don't "complete the square" for a cubic

let's look at the graph of
y = x^3 - 2x^2 - 16 to see if it worth doing

http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E3-2x%5E2-16

looks like there is only one real root.

Have you learned a method to solve a cubic equation?
Wolfram says there is a real root at
x = appr 3.3912

http://www.wolframalpha.com/input/?i=x%5E3-2x%5E2-16%3D0