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Cube root. In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other ...
The case shown has two critical points. Here the function is . In algebra, a cubic equation in one variable is an equation of the form. in which a is nonzero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are ...
Square root. Notation for the (principal) square root of x. For example, √ 25 = 5, since 25 = 5 ⋅ 5, or 52 (5 squared). In mathematics, a square root of a number x is a number y such that ; in other words, a number y whose square (the result of multiplying the number by itself, or ) is x. [1] For example, 4 and −4 are square roots of 16 ...
The cube root law is an observation in political science that the number of members of a unicameral legislature, or of the lower house of a bicameral legislature, is about the cube root of the population being represented. [1] The rule was devised by Estonian political scientist Rein Taagepera in his 1972 paper "The size of national assemblies".
Halley's method. In numerical analysis, Halley's method is a root-finding algorithm used for functions of one real variable with a continuous second derivative. Edmond Halley was an English mathematician and astronomer who introduced the method now called by his name. The algorithm is second in the class of Householder's methods, after Newton's ...
The volume of a geometric cube is the cube of its side length, giving rise to the name. The inverse operation that consists of finding a number whose cube is n is called extracting the cube root of n. It determines the side of the cube of a given volume. It is also n raised to the one-third power. The graph of the cube function is known as the ...
Roots of unity can be defined in any field. If the characteristic of the field is zero, the roots are complex numbers that are also algebraic integers. For fields with a positive characteristic, the roots belong to a finite field, and, conversely, every nonzero element of a finite field is a root of unity.
The roots, stationary points, inflection point and concavity of a cubic polynomial x 3 − 6x 2 + 9x − 4 (solid black curve) and its first (dashed red) and second (dotted orange) derivatives. The critical points of a cubic function are its stationary points, that is the points where the slope of the function is zero.