# Where does the word “roots” come from when talking about zeros

We often use the word roots when referring to the solutions of an equation. For instance, when we have a polynomial $P(x)$, we call its zeros the roots of $P(x)$.

For some polynomials we can relate the zeros with a root function of some kind, say $$x^2-4=0,$$ we can take the square roots of $4$ to get the solutions. However with some functions, like trigonometrics, there doesn't seem to be a clear relation with the typical root functions.

I ask because in an assignment I gave, students where asked to find the roots of a rational function. I found out that many students had never heard the word roots used in a "find the zeros" context. Many of them took the square roots of the function and tried solving some equations that made no sense.

When looking online, I could not find any solid reference to the first uses of the word in that context.

• mathforum.org/library/drmath/view/71575.html – Dag Oskar Madsen Sep 30 '14 at 16:56
• Thanks @DagOskarMadsen, if you are willinf to turn parts of the text linked into an answer, I'll accept it. – Jean-Sébastien Sep 30 '14 at 18:39
• I was always taught that functions have zeros, equations have solutions, graphs have x-intercepts and polynomials (as in their own right distinct from the concept of function) have roots. – DavidButlerUofA Sep 30 '14 at 19:51

Doctor Peterson in The Math Forum refers to the following sources.

From D. E. Smith, History Of Mathematics Vol II (1925), footnote page 393:

The Arabs also used jidr (dyizr, root), whence the Latin radix.

A longer quote from W. W. R. Ball, A Short Account of the History of Mathematics (4th edition, 1908):

The algebra of Alkarismi holds a most important place in the history of mathematics, for we may say that the subsequent Arab and the early medieval works on algebra were founded on it, [...]. The unknown quantity is termed either "the thing" or "the root" (that is, of a plant), and from the latter phrase our use of the word root as applied to the solution of an equation is derived. The square of the unknown is called "the power".

• Many accolades to you for finding the specific citation! – Chris Cunningham Sep 30 '14 at 19:16
• It was a simple Google search :) Both books are available online. – Dag Oskar Madsen Sep 30 '14 at 19:19
• I had found a similar page by Dr Peteron, but it was not as precise. I tossed other results in google because of that. Shame on me, woot for you! – Jean-Sébastien Sep 30 '14 at 19:51
• @Jean-Sébastien I meant finding the books with the citations was a simple Google search – Dag Oskar Madsen Sep 30 '14 at 19:55