"Root of a function" redirects here. For a half iterate of a function, see Functional square root.
A graph of the function for in , with zeros at , and marked in red.
In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function , is a member of the domain of such that vanishes at ; that is, the function attains the value of 0 at , or equivalently, is a solution to the equation .[1] A "zero" of a function is thus an input value that produces an output of 0.[2]
A root of a polynomial is a zero of the corresponding polynomial function.[1] The fundamental theorem of algebra shows that any non-zero polynomial has a number of roots at most equal to its degree, and that the number of roots and the degree are equal when one considers the complex roots (or more generally, the roots in an algebraically closed extension) counted with their multiplicities.[3] For example, the polynomial of degree two, defined by has the two roots (or zeros) that are 2 and 3.
If the function maps real numbers to real numbers, then its zeros are the -coordinates of the points where its graph meets the x-axis. An alternative name for such a point in this context is an -intercept.
^ ab"Algebra - Zeroes/Roots of Polynomials". tutorial.math.lamar.edu. Retrieved 2019-12-15.
^Foerster, Paul A. (2006). Algebra and Trigonometry: Functions and Applications, Teacher's Edition (Classics ed.). Upper Saddle River, NJ: Prentice Hall. p. 535. ISBN 0-13-165711-9.
^"Roots and zeros (Algebra 2, Polynomial functions)". Mathplanet. Retrieved 2019-12-15.
and 24 Related for: Zero of a function information
mathematics, azero (also sometimes called a root) ofa real-, complex-, or generally vector-valued function f {\displaystyle f} , is a member x {\displaystyle...
called zero elements.) Examples include identity elements of additive groups and vector spaces. Another example is the zerofunction (or zero map) on a domain...
singularity of such afunction (see essential singularity). Technically, a point z0 is a pole ofafunction f if it is azeroof the function 1/f and 1/f...
Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value is zero everywhere...
a loss function or cost function (sometimes also called an error function) is afunction that maps an event or values of one or more variables onto a...
contained the Riemann hypothesis, a conjecture about the distribution of complex zerosof the Riemann zeta function that many mathematicians consider...
Azero-crossing is a point where the sign ofa mathematical function changes (e.g. from positive to negative), represented by an intercept of the axis...
the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real...
that is, a polynomial functionof degree zero or one. For distinguishing such a linear function from the other concept, the term affine function is often...
tends to some value. When a real function can be expressed as a fraction whose denominator tends to zero, the output of the function becomes arbitrarily large...
statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen...
with zero, then the result is a quadratic equation. The solutions ofa quadratic equation are the zerosof the corresponding quadratic function. The bivariate...
is an absorbing element under Cartesian product of sets, since { } × S = { } The zerofunction or zero map defined by z(x) = 0 under pointwise multiplication...
The exponential function is a mathematical function denoted by f ( x ) = exp ( x ) {\displaystyle f(x)=\exp(x)} or e x {\displaystyle e^{x}} (where...
property, the zerosof the normalized sinc function are the nonzero integer values of x. The normalized sinc function is the Fourier transform of the rectangular...
plane except zero and the negative integers, where the function has simple poles.[clarification needed] The gamma function has no zeros, so the reciprocal...
incomplete gamma function, which is defined as an integral from zero to a variable upper limit. Similarly, the upper incomplete gamma function is defined as...
analytic function is afunction that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions...
continuous function f, an interval [a, b], and the function values f(a) and f(b). The function values are of opposite sign (there is at least one zero crossing...
= 0 or azeroof the polynomial function defined by P. In the case of the zero polynomial, every number is azeroof the corresponding function, and the...
and has zero derivative almost everywhere, its value still goes from 0 to 1 as its argument reaches from 0 to 1. Thus, in one sense the function seems very...
has a slope that is non-zero but finite, such that the graph of the function approaches it as x tends to +∞ or −∞. More generally, one curve is a curvilinear...
The Flipper Zero is a portable Tamagotchi-like multi-functional device developed for interaction with access control systems. The device is able to read...
indicator function or a characteristic functionofa subset ofa set is afunction that maps elements of the subset to one, and all other elements to zero. That...
Global Information
![{\displaystyle \left[-2\pi ,2\pi \right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cdc6c1efef56b12d350b9e16f34e39e317d5b51f)
