If 1, 3, 4, 0 are the roots of $a{x}^4+b{x}^3+c{x}^2+dx+e=0$ then the roots of $a{(x+3)}^4+b{(x+3)}^3+c{(x+3)}^2+d(x+3)+e=0$ are

 $f\left(x\right)=a{x}^4+b{x}^3+c{x}^2+dx+e=0$  roots are 1,3,4,0

 $then f\left(x+3\right)=a{(x+3)}^4+b{(x+3)}^3+c{(x+3)}^2+d(x+3)+e=0$

 roots are decreased by ‘3’.

 therefore roots of the $f\left(x+3\right)=0$  are : –2,0,1, $-$ 3