- Root (mathematics)
In other words, a "root" of a function is a value for that produces a result of zero ("0"). For example, consider the function defined by the following formula::This function has a root at 3 because .
If the function is mapping from
real numbers to real numbers, its zeros are the points where its graph meets the "x"-axis. The x-value of such a point is called x-intercept. Therefore in this situation a root can be called an "x"-intercept.
The word root can also refer to the
nth rootof a number, a, as in .The square rootof a number,a, is .
A substantial amount of mathematics was developed in order to find roots of various functions, especially
polynomials. One wide-ranging concept, complex numbers, was developed to handle the roots of quadratic or cubic equations with negative discriminant(that is, those leading to expressions involving the square root of negative numbers).
All real polynomials of odd degree have a real number as a root. Many real polynomials of even degree do not have a real root, but the
fundamental theorem of algebrastates that every polynomial of degree has complex roots, counted with their multiplicities. The non-real roots of polynomials with real coefficients come in conjugate pairs. Vieta's formulasrelate the coefficients of a polynomial to sums and products of its roots.
One of the most important
unsolved problems in mathematicsconcerns the location of the roots of the Riemann zeta function.
zero (complex analysis)
pole (complex analysis)
* other roots
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