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The plus-minus sign (±) is a mathematical symbol commonly used to indicate the precision of an approximation, or as a convenient shorthand for a quantity with two possible values.
This second usage is perhaps most commonly encountered in the well-known formula for the solutions of quadratic equations: if <math>ax^2 + bx + c = 0<math>, then
- <math>
x = \frac{-b \pm \sqrt {b^2-4ac\ }}{2a}.
<math>
In other words, the two solutions to the equation are
- <math>
x = \frac{-b + \sqrt {b^2-4ac\ }}{2a}
<math>
and
- <math>
x = \frac{-b - \sqrt {b^2-4ac\ }}{2a}
<math>
but using the ± symbol allows us to compress these expressions into a single formula.
The use of ± for an approximation is closely related. For example, "5 ± 0.2" denotes a quantity that is within 0.2 units of 5; it is between 5 - 0.2 and 5 + 0.2.
In Unicode, the plus-minus symbol is given by the code U+00B1, and its HTML representation is ±. There is also another character, minus-or-plus sign (∓); its codepoint is U+2213. This is rarely seen; it can be used alongside "±" in such expressions as "x ± y ∓ z", which can be interpreted as "x + y - z" or "x - y + z", but not "x + y + z" or "x - y - z". The upper "-" in "∓" is considered attached to the "+" of "±" (and the lower symbols work in the same way) even though there is no visual indication of the dependency. The original expression can be rewritten as "x ± (y - z)" to avoid confusion.
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