If $x^3+3x^2-9x+c$  is of the form of ${\left(x-\alpha \right)}^2\left(x-\beta \right)$  then the positive value of c is _____

Here $x=\alpha$  is repeated root of the equation $f\left(x\right)=0$

hence $x=\alpha$  is also a root of the equation $f^I\left(x\right)=0$  i.e., $3x^2+6x-9=0$

$or{x}^2+2x-3=0or\left(x+3\right)\left(x-1\right)=0$

has the root $\alpha$  once which can be either $-3or1$

$If\alpha =1,thenf\left(x\right)=0givesc-5=0orc=5$

$If\alpha =-3thenf\left(x\right)=0gives-27+27+27+c=0$

$\therefore c=-27$