Okay, this is something that's been bugging me for a while. A lot of the polynomials with higher powers can't be solved using algebraic methods and must be estimated. So my idea was to take these answers and find a way to convert them into an exact form, such as quadratic irrationals/surds.(adsbygoogle = window.adsbygoogle || []).push({});

I do not know if all zeroes of polynomials can be represented as quadratic irrationals. However, I did find out that you can use continued fractions to get a quadratic irrational solution from its decimal value to its [itex]\dfrac{a + b\sqrt{c}}{d}[/itex] form.

The problem I'm having with continued fractions is that you have to keep going until you find where they repeat, for many quadratic irrationals there are dozens of numbers in the series, and I don't have enough accuracy in my calculations to find where it repeats.

And then of course there's guess and check, but I don't know a way of doing it efficiently yet.

So what should I do?

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# Finding quadratic irrationals from their decimal form

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