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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 ...
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 ...
Nested radical. In algebra, a nested radical is a radical expression (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression. Examples include. which arises in discussing the regular pentagon, and more complicated ones such as.
Cubic function. Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis—where y = 0). The case shown has two critical points. Here the function is f(x) = (x3 + 3x2 − 6x − 8)/4. In mathematics, a cubic function is a function of the form that is, a polynomial function of degree three.
An illustration of Newton's method. In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real -valued function. The most basic version starts with a real-valued ...
Laguerre's method. In numerical analysis, Laguerre's method is a root-finding algorithm tailored to polynomials. In other words, Laguerre's method can be used to numerically solve the equation p(x) = 0 for a given polynomial p(x). One of the most useful properties of this method is that it is, from extensive empirical study, very close to being ...
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 ...
Muller's method. Muller's method is a root-finding algorithm, a numerical method for solving equations of the form f (x) = 0. It was first presented by David E. Muller in 1956. Muller's method is based on the secant method, which constructs at every iteration a line through two points on the graph of f. Instead, Muller's method uses three ...
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