The number of distinct real roots of the equation $3x^4+4x^3-12x^2+4=0$  is _____

$3x^4+4x^3-12x^2+4=0$ . Let  $f\left(x\right)=3x^4+4x^3-12x^2+4$.
 $f\text{'}\left(x\right)=12x^3+12x^2-24x=12x(x^2+x-2)=12x(x+2)(x-1)$
 $\therefore$ f(x) is increasing on  $(-2,0)\cup (1,\infty )$ and decreasing on  $(-\infty ,-2)\cup (0,1)$
$\therefore$ The number of distinct real roots of $f\left(x\right)=0$  is 4