If $k\sqrt{-1}$  is a root of the equation $x^4+6x^3-16x^2+24x-80=0$ , then $k=$

Replace $x$  with $2i$  then the equation is

$f\left(2i\right)={\left(2i\right)}^4+6{\left(2i\right)}^3-16{\left(2i\right)}^2+24\left(2i\right)-80=0$

$=16-48i+64+48i-80=0$

$\therefore 2i$  is a factors of $f\left(x\right)$

Given $k\sqrt{-1}$  is a factor of $f\left(x\right)$

$\therefore k=\pm 2$