When using 64 bit floating point numbers with 54 bits of precision, (or likely in this case, complex values consisting of two 64 bit floats) and you use an algorithm which you can guarantee converges to within 55 bits of precision in X steps, you have found the closest representable solution. Yes, you don't know whether it's 1 + sqrt(17) or 0.9 + Sqrt[17.84...], but you know to a degree of precision that 95% of use cases need what the value is. I do understand what you are saying, but the parent comment was referring to a student factoring polynomials. You doubted what he did based on the fact that he couldn't exactly specify what the roots were. I just assumed that he likely found the roots to a reasonable accuracy and then factored with these approximated values. The parent never specified, but given doubting the authenticity of the comment or celebrating youthful ingenuity, I choose the latter. I understand what you are saying. Yes, you can not find the EXACT values of the roots, but within the context of this comment chain, I don't think that matters.