Pertubation of Roots

f[x_] = x^8 - 36 x^7 + 546 x^6 - 
4536 x^5 + 22449 x^4 - 67284 x^3 + 118124 x^2 - 109584 x + 40320

Factor[%]

Plot[f[x],{x,0,10}]

g[x_] = x^8 - 36.001 x^7 + 546 x^6 - 
4536 x^5 + 22449 x^4 - 67284 x^3 + 
118124 x^2 - 109584 x + 40320

Factor[%]

Plot[g[x],{x,0,10}]