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All published worksheets from http://sagenb.org

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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)]