The range of values of  " a " so that the equation $x^3-3x+a=0$ has three real and distinct roots is  

Let, $f\left(x\right)=x^3-3x+a\Rightarrow f\text{'}\left(x\right)=3x^2-3=3(x-1)(x+1)$

Now, $f\left(1\right)=a-2,f(-1)=a+2$

The roots would be real and distinct if, 

$f\left(1\right)f(-1)<0\Rightarrow (a-2)(a+2)<0or\Rightarrow -2<a<2$

Thus the given equation would have real and distinct roots if  $a\in (-2,2)$