This has been something that in all of my years of mathematics, I haven't ever questioned. Is there any connection to the word 'root' in the context of function roots (e.g. polynomial roots) and nth roots?
In the context of taking the nth root of a number, it's essentially asking 'what number can be raised by n to equal x?'. Thus the 2 root of 32 is asking, 'x^2 = 32: solve for x'
Now in the context of function roots, it's asking 'for what value of the independent variable does the function equal zero?'.
So my question: What's the significance of the word 'root'? What's the history of this word? Why's it being applied to two seemingly different things?
Thanks,
Any formula that asks you to find the n'th root of a number such as $ \sqrt[k]{a} $ can be transformed into an equivalent polynomial root problem $ f(x) = x^k - a = 0$. So finding the n'th root is a special case of the general polynomial root.