root

If a function f(x) has the value 0 for x = a, a is a root of the equation f(x) = 0. The fundamental theorem of algebra states that any algebraic equation of the form a₀xⁿ + a₁xⁿ⁻¹ + ··· a_n−1x + a_n = 0, where the a_k's are real numbers, has at least one root. From this it follows readily that such an equation has roots, real or complex, in number equal to the index (here n) of the highest power of x.

Furthermore, if a + ib (where i = Ö−1) is a complex root of the given equation, so is a − ib, the conjugate of a + ib. Equations of degrees up to four may be solved algebraically. This statement means that the roots may be expressed as functions of the coefficients, the functions involving the elementary arithmetical processes of addition, multiplication, raising a number to a power, or extracting the root of a certain order of a given number. It was proved by H. Abel and by E. Galois that it is not possible to solve algebraically the general algebraic equation of degree higher than four. However, it is possible to determine the real roots of an algebraic equation to any desired degree of approximation. See also Calculus; Equations, theory of; Numerical analysis.

(1) The top level of a hierarchy. See tree, root directory and root domain.

(2) A person with unlimited access privileges who can perform any and all operations on the computer. Also called "superuser."

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1. the part of a human tooth covered by cementum. n 2. a nerve root; the part of a nerve adjacent to the center with which it is connected; in spinal and cranial nerves the part of the nerve between the cells of origin or termination and the ganglion.

In mathematics, the term root can mean:

• The square root, the cube root, or more generally the nth root of a number.
• Any solution to a mathematical equation (see equation solving).
• A root of a function, i.e. an x-value for which the function produces a result of zero.
• A root of unity, a complex number which is an nth root of one.
• In graph theory, a rooted tree is tree with a distinguished node called the root.
• A root system of vectors, whose elements are called roots.

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