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A cube root of a number x is a number y such that y3 = x. Learn about the real and complex cube roots, their formal definition, geometric representation, numerical methods and applications in mathematics.
Learn about the origins and solutions of cubic equations, which are equations of the form ax3 + bx2 + cx + d = 0. Find out how ancient and medieval mathematicians from different cultures approached and solved cubic equations using algebra, geometry, and numerical approximations.
X is a fixed-point of if and only if x is a root of , and x is an ε-residual fixed-point of if and only if x is an ε-root of . Chen and Deng [ 18 ] show that the discrete variants of these problems are computationally equivalent: both problems require Θ ( n d − 1 ) {\displaystyle \Theta (n^{d-1})} function evaluations.
Theta functions are special functions of several complex variables that appear in various topics of mathematics. Learn about their definitions, properties, identities, representations, and applications in elliptic functions, modular forms, and quantum field theory.
Symbolab is a website that provides step-by-step solutions to mathematical problems in various subjects. It was developed by an Israeli company and acquired by Course Hero in 2020.
A cube is the third power of a number, denoted by a superscript 3. Learn about the cube function, the cube root, the cubic parabola, and the perfect cubes in integers and base ten.
Learn about the definition, properties and applications of zeros of functions, also known as roots of polynomials or solutions of equations. Find out how to compute zeros, their number and multiplicity, and their relation to algebraic geometry and analysis.
Learn how to solve quadratic equations using the quadratic formula, a closed-form expression that describes the roots of a quadratic function. Explore different methods of deriving the formula, such as completing the square, substitution, and Lagrange resolvents.