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For example, would solving for $x$ in $x^2=8x+7$ be the same as finding the roots of the equation? Also, would finding the roots of this be the same as finding the zeros?

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    Just thinking out loud but could it be that a "root" (b/c square root, cube root, etc.) only applies to polynomials, while solutions/zeros could also apply to linear/trig equations?2013-11-26

1 Answers 1

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For the following pattern:

(roots of|zeros of|solutions to) (an equation|a function).

currently, the preferred usage is (in order):

  • roots of an equation.
  • zeros of a function.
  • solutions to an equation.
  • roots of a function.

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"zeros of an equation" and "solutions to a function" are just plain wrong.

Presumably if one is talking about an equation, then 'roots' is preferred (or rather, it is just how people happen to speak).

This is all to say that these phrases are all interchangeable, but some are preferred to others in their contexts.

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    you have a point, but I'd say that mathematical language is judged by a $\it weighted$ majority vote, where some of us have weightier votes than others. A similar chart based on usage in Inventiones might have a different look.2011-05-07