Need to find the roots of the polynomial equation

x^3-5x^2+7x-35 = 0

I got:

f(1)=-32

f(-1)=-48

f(1/5)=-33

f(-1/5)=-36

f(1/7)=-34

f(-1/7)=-36

f(1/35)=-34

f(-1/35)=-35

I didn't bother rounding decimals but, I got no rational roots.. so If someone could verify this answer? Since my book does not have an answer key...