Why is the study of finding roots of polynomials so important? I know some basic applications of finding roots of quadratic equations (eg. where will a projectile land after being fired, etc...) but it seems that finding roots has a special importance in math (algebra, number theory???, inability to solve roots of quintic and higher polynomials). Why?

Question

Why is the study of finding roots of polynomials so important?  I know some basic applications of finding roots of quadratic equations (eg. where will a projectile land after being fired, etc...) but it seems that finding roots has a special importance in math (algebra, number theory???, inability to solve roots of quintic and higher polynomials).  Why?

anonymous · Answer

Mainly because of it's historical importance, their study having led to modern abstract algebra.

I would suggest that their in depth study is more likely of use to pure mathematicians these days.

There has always been a tendency in mathematics to (try and) teach students everything that has ever been learned in mathematics from Euclid on up.

anonymous · Answer

Thank you.  This question may not make sense but when you take into account complex roots and the fundamental theorem of algebra, does the set of all polynomials, or maybe the set of polynomials of the same order, have an order relation on it?  In other words, can polynomials be counted in an order?  Would this be important?

anonymous · Answer

I have no idea (I don't much care either:-)