The number for "nothing", written 0; it is neither positive nor negative.
Precisely: The integer 0: the additive identity (a + 0 = a) and the number that makes any product 0 (a × 0 = 0).
How it works
Indian thinkers called emptiness śhūnya; Brahmagupta (628 CE) made it a number with rules: a − a = 0, a + 0 = a, a × 0 = 0. Dividing by zero has no meaning.
Examples
Brahmagupta's rule says a fortune minus the same fortune is zero.
The origin on the coordinate plane is where both coordinates are zero.
5 ÷ 0 is not defined, because no number times zero gives 5.
Do not confuse: 0 in 105 is a place holder and also a number; "nothing" in everyday talk is not the same as the number 0 in a calculation.
Used in
place value (the 0 in 105), integers, coordinates and number lines
History: Brahmagupta, Brāhmasphuṭasiddhānta (628 CE), rules for zero
zero of a polynomial
ZEER-oh uv uh pol-ee-NOH-mee-ulClass 9
A number that makes the polynomial equal to 0 when you put it in for x.
Precisely: A real number k is a zero of the polynomial p(x) when p(k) = 0; on the graph of y = p(x), it is the x-coordinate of a point where the graph meets the x-axis.
How it works
Put the number into the polynomial and work it out: if the answer is 0, it is a zero. To find zeroes, factorise and set each factor equal to 0. A polynomial of degree n has at most n zeroes.
Examples
−1 and 4 are the zeroes of x² − 3x − 4, because p(−1) = 0 and p(4) = 0.
The zero of a polynomial 2x + 3 is −3/2, where its line crosses the x-axis.
2x² − 8x + 6 = 2(x − 1)(x − 3), so its zeroes are 1 and 3; their sum is 4 = 8/2 and their product 3 = 6/2.
The cubic x³ − 4x = x(x − 2)(x + 2) has three zeroes: −2, 0 and 2.
Do not confuse: A zero of a polynomial is an input that gives 0, not the value 0 itself; p(0), the value at x = 0, is a different thing (for x² − 3x − 4 it is −4).
Used in
factorising, solving equations, graphs of polynomials, the sum and product of zeroes