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In some contexts, particularly when the number whose cube root is to be taken is a real number, one of the cube roots (in this particular case the real one) is referred to as the principal cube root, denoted with the radical sign The cube root is the inverse function of the cube function if considering only real numbers, but not if considering also complex numbers: although one has always the ...
Here the function is and therefore the three real roots are 2, −1 and −4. In algebra, a cubic equation in one variable is an equation of the form in which a is not zero. 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 ...
The geometric mean can be understood in terms of geometry. The geometric mean of two numbers, and , is the length of one side of a square whose area is equal to the area of a rectangle with sides of lengths and . Similarly, the geometric mean of three numbers, , , and , is the length of one edge of a cube whose volume is the same as that of a ...
In mathematics, a cubic function is a function of the form that is, a polynomial function of degree three. In many texts, the coefficients a, b, c, and d are supposed to be real numbers, and the function is considered as a real function that maps real numbers to real numbers or as a complex function that maps complex numbers to complex numbers.
Generalization to rings Vieta's formulas are frequently used with polynomials with coefficients in any integral domain R. Then, the quotients belong to the field of fractions of R (and possibly are in R itself if happens to be invertible in R) and the roots are taken in an algebraically closed extension.
In mathematics, an nth root of a number x is a number r (the root) which, when raised to the power of the positive integer n, yields x: The integer n is called the index or degree, and the number x of which the root is taken is the radicand. A root of degree 2 is called a square root and a root of degree 3, a cube root.
Rationalisation (mathematics) In elementary algebra, root rationalisation (or rationalization) is a process by which radicals in the denominator of an algebraic fraction are eliminated. If the denominator is a monomial in some radical, say with k < n, rationalisation consists of multiplying the numerator and the denominator by and replacing by ...
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.