Since h(x) represents the height of a kangaroo x seconds after it jumps, then the kangaroo is on the ground when h(x)=0.
Now, notice that:
[tex]-6x^3+12x^2=-6x^2(x-2).[/tex]Then:
[tex]h(x)=0\text{ if and only if }-6x^2=0\text{ or }x-2=0.[/tex]Therefore:
[tex]h(x)=0\text{ if and only if }x=0\text{ or }x=2.[/tex]Then the kangaroo is in air for 2 seconds.
Answer: 2 seconds.
