Wherever I look on the internet I find the statement of fundamental theorem of algebra like:
Every non-constant single-variable polynomial with complex coefficients has at least one complex root.
While in school times and in the sources where the target audience are grade school students it is stated like:
Every non-zero, single-variable, degree $n$ polynomial with complex coefficients has, counted with multiplicity, exactly $n$ complex roots.
Although both of these statements are identical but I can't seem to understand the reason why it is usually presented in the manner of the former definition which appears, at least to me, a little less intuitive than the later one.
I guess the reason might be the factor of multiplicity concerned in the later definition but I would like to reflect upon what do you think about this issue.
I first thought not to cite any sources at all since the definitions are versatile on internet but upon reading the comments I changed my mind. So, FYI, I got the first definition at https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra, http://mathworld.wolfram.com/FundamentalTheoremofAlgebra.html, https://www.math.ucdavis.edu/~anne/WQ2007/mat67-Ld-FTA.pdf, https://brilliant.org/wiki/fundamental-theorem-of-algebra/, http://www.mathwords.com/f/fundamental_thm_algebra.htm, https://people.richland.edu/james/lecture/m116/polynomials/theorem.html and https://www.youtube.com/watch?v=shEk8sz1oOw
and second one at https://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html, http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Fund_theorem_of_algebra.html, https://www.britannica.com/topic/fundamental-theorem-of-algebra, my grade school book(NCERT book and related reference books) and most of the sources given for the first definition.
And yes, wording of the definitions I've provided are taken directly from Wikipedia.