4840.sagews

f=x^2-2*x+1

f.roots(ring=RealField())

[(1.00000000000000, 2)]

f1=x^2-2*x+1+10^(-20)

f1.roots(ring=RealField())

[(1.00000000000000, 2)]

f2=x^2-2*x+1+10^(-10)

f2.roots(ring=RealField())

[]

f3=x^2-2*x+1-10^(-10)

f3.roots(ring=RealField())

[(0.999989999999586, 1), (1.00001000000041, 1)]

f4=x^2-2*x+1-10^(-14)

f4.roots(ring=RealField())

[(0.999999900039972, 1), (1.00000009996003, 1)]