# What is the time complexity in solving a polynomial equation of degree N in one variable?

How easy/difficult(in terms of big-O) is it to solve polynomial equations of high degrees of N?

Do apps like Desmos actually solve equations to get roots or do they approximate roots by iterating through a range of values for x?

What mechanisms are at play in solving a univariate polynomial equation algorithmically?

• What do you mean by solving? How is the solution represented? – Yuval Filmus Dec 1 '19 at 12:07
• By "solving" I mean obtaining a list of all its real roots – Akshay Vasudeva Rao Dec 1 '19 at 12:33
• How are the solutions represented? Even assuming that the coefficients are integers, the solutions need not be rational. Perhaps you want, given some $\epsilon > 0$, a list of all roots up to error $\epsilon$? – Yuval Filmus Dec 1 '19 at 12:59
• – D.W. Dec 1 '19 at 18:18
• @D.W. Thanks! That helped :) – Akshay Vasudeva Rao Dec 2 '19 at 6:34