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Polynomial equation of degree two
In mathematics, a quadratic equation (from Latin quadratus 'square') is an equation that can be rearranged in standard form as a x 2 + b x + c = 0 , {\displaystyle
Quadratic_equation
Formula that provides the solutions to a quadratic equation
algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic equations,
Quadratic_formula
Topics referred to by the same term
Look up quadratic in Wiktionary, the free dictionary. In mathematics, the term quadratic describes something that pertains to squares, to the operation
Quadratic
Polynomial with all terms of degree two
In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, 4 x
Quadratic_form
Polynomial function of degree two
In mathematics, a quadratic function of a single variable is a function of the form f ( x ) = a x 2 + b x + c {\displaystyle f(x)=ax^{2}+bx+c} with
Quadratic_function
Algebraic structure in mathematics
mathematics, a quadratic algebra is an algebra over a ring for which the algebra extends the ring by a new element that satisfies a monic, quadratic polynomial
Quadratic_algebra
Solving an optimization problem with a quadratic objective function
Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks
Quadratic_programming
Mathematical proportionality to a square
said to exhibit quadratic growth when its values are proportional to the square of the function argument or sequence position. "Quadratic growth" often
Quadratic_growth
Theory extending Einstein gravity
Quadratic gravity (QG) is an extension of general relativity obtained by adding all local quadratic-in-curvature terms to the Einstein–Hilbert Lagrangian
Quadratic_gravity
Field (mathematics) generated by the square root of an integer
theory, a quadratic field is an algebraic number field of degree two over Q {\displaystyle \mathbf {Q} } , the rational numbers. Every such quadratic field
Quadratic_field
In mathematics, a quadratic differential on a Riemann surface is a section of the symmetric square of the holomorphic cotangent bundle. If the section
Quadratic_differential
Optimization problem in mathematics
quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions
Quadratically constrained quadratic program
Quadratically_constrained_quadratic_program
Type of homogeneous polynomial of degree 2
In mathematics, a definite quadratic form is a quadratic form over some real vector space V that has the same sign (always positive or always negative)
Definite_quadratic_form
Quantity defined for a stochastic process
mathematics, quadratic variation is used in the analysis of stochastic processes such as Brownian motion and other martingales. Quadratic variation is
Quadratic_variation
Gives conditions for the solvability of quadratic equations modulo prime numbers
theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime
Quadratic_reciprocity
Sum type in number theory
In number theory, quadratic Gauss sums are certain finite sums of roots of unity. A quadratic Gauss sum can be interpreted as a linear combination of
Quadratic_Gauss_sum
Curve used in computer graphics and related fields
Pn, where n is called the order of the curve (n = 1 for linear, 2 for quadratic, 3 for cubic, etc.). The first and last control points are always the
Bézier_curve
Linear optimal control technique
by a quadratic function is called the LQ problem. One of the main results in the theory is that the solution is provided by the linear–quadratic regulator
Linear–quadratic_regulator
Integer that is a perfect square modulo some integer
In number theory, an integer q is a quadratic residue modulo n if it is congruent to a perfect square modulo n; that is, if there exists an integer x
Quadratic_residue
Collective decision-making procedure
Quadratic voting (QV) is a voting system that encourages voters to express their true relative intensity of preference (utility) between multiple options
Quadratic_voting
Method for solving quadratic equations
elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form a x 2 + b x + c {\displaystyle \textstyle ax^{2}+bx+c}
Completing_the_square
Root of a quadratic polynomial with a unit leading coefficient
number theory, quadratic integers are a generalization of the usual integers to quadratic fields. A complex number is called a quadratic integer if it
Quadratic_integer
Address collision resolution scheme
Quadratic probing is an open addressing scheme in computer programming for resolving hash collisions in hash tables. Quadratic probing operates by taking
Quadratic_probing
Mathematical concept
quadratic irrational number (also known as a quadratic irrational or quadratic surd) is an irrational number that is the solution to some quadratic equation
Quadratic_irrational_number
Measure of variation in statistics
_{i=1}^{N}\left(x_{i}-{\bar {x}}\right)^{2}}},} The error in this approximation decays quadratically (as 1/N2), and it is suited for all but the smallest samples or highest
Standard_deviation
Method of solving equations
In numerical analysis, inverse quadratic interpolation is a root-finding algorithm, meaning that it is an algorithm for solving equations of the form
Inverse quadratic interpolation
Inverse_quadratic_interpolation
1993 Canadian TV series or program
Quadratics is a six-part Canadian instructional television series produced by TVOntario in 1993. The miniseries is part of the Concepts in Mathematics
Quadratics
quadratic Jordan algebras are a generalization of Jordan algebras introduced by Kevin McCrimmon (1966). The fundamental identities of the quadratic representation
Quadratic_Jordan_algebra
Listing all imaginary quadratic fields with a given class number
problem (for imaginary quadratic fields), as usually understood, is to provide for each n ≥ 1 a complete list of imaginary quadratic fields Q ( d ) {\displaystyle
Class_number_problem
Problem in computational number theory
The quadratic residuosity problem (QRP) in computational number theory is to decide, given integers a {\displaystyle a} and N {\displaystyle N} , whether
Quadratic_residuosity_problem
Combinatorial optimization problem
The quadratic assignment problem (QAP) is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research
Quadratic_assignment_problem
Integer factorization algorithm
The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second-fastest method known (after the general number field
Quadratic_sieve
The quadratic knapsack problem (QKP), first introduced in 19th century, is an extension of knapsack problem that allows for quadratic terms in the objective
Quadratic_knapsack_problem
Topics referred to by the same term
In mathematics, a quadratic transformation may be A quadratic transformation in the Cremona group Kummer's quadratic transformation of the hypergeometric
Quadratic_transformation
Curve from a cone intersecting a plane
A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola
Conic_section
In number theory, the law of quadratic reciprocity, like the Pythagorean theorem, has lent itself to an unusually large number of proofs. Several hundred
Proofs of quadratic reciprocity
Proofs_of_quadratic_reciprocity
Statistical classifier in machine learning
In statistics, a quadratic classifier is a statistical classifier that uses a quadratic decision surface to separate measurements of two or more classes
Quadratic_classifier
Mathematical relation assigning a probability event to a cost
regression theory, which is based on the quadratic loss function. The quadratic loss function is also used in linear-quadratic optimal control problems. In these
Loss_function
Estimate of time taken for running an algorithm
general-purpose sorts run in linear time, but the change from quadratic to sub-quadratic is of great practical importance. An algorithm is said to be of
Time_complexity
Field of mathematics and science based on non-linear systems and initial conditions
showed that, at least for dissipative and conservative quadratic systems, three-dimensional quadratic systems with only three or four terms on the right-hand
Chaos_theory
Function whose squared absolute value has finite integral
In mathematics, a square-integrable function, also called a quadratically integrable function or L 2 {\displaystyle L^{2}} function or square-summable
Square-integrable_function
Mathematical concept
genus is a classification of quadratic forms and lattices over the ring of integers. An integral quadratic form is a quadratic form on Zn, or equivalently
Genus_of_a_quadratic_form
In mathematics, the quadratic eigenvalue problem (QEP), is to find scalar eigenvalues λ {\displaystyle \lambda } , left eigenvectors y {\displaystyle
Quadratic_eigenvalue_problem
Circle associated with a quadratic equation
associated with a quadratic equation; it is named after Thomas Carlyle. The circle has the property that the solutions of the quadratic equation are the
Carlyle_circle
Optimization algorithm
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization, also known as Lagrange-Newton method. SQP methods
Sequential quadratic programming
Sequential_quadratic_programming
Quadratic homogeneous polynomial in two variables
In mathematics, a binary quadratic form is a quadratic homogeneous polynomial in two variables q ( x , y ) = a x 2 + b x y + c y 2 , {\displaystyle q(x
Binary_quadratic_form
numbers is quadratically closed; more generally, any algebraically closed field is quadratically closed. The field of real numbers is not quadratically closed
Quadratically_closed_field
Basic concepts of algebra
be quadratic but linear). Because of this a quadratic equation must contain the term a x 2 {\displaystyle ax^{2}} , which is known as the quadratic term
Elementary_algebra
In mathematics, a quadratic set is a set of points in a projective space that bears the same essential incidence properties as a quadric (conic section
Quadratic_set
Quadratic form for which there is a non-zero vector on which the form evaluates to zero
In mathematics, a quadratic form over a field F is said to be isotropic if there is a non-zero vector on which the form evaluates to zero; otherwise,
Isotropic_quadratic_form
Mathematical concept
mathematics, specifically the theory of quadratic forms, an ε-quadratic form is a generalization of quadratic forms to skew-symmetric settings and to
Ε-quadratic_form
Natural number
arithmetic Chinese remainder theorem Arithmetic functions Advanced concepts Quadratic forms Modular forms L-functions Diophantine equations Diophantine approximation
1
Quadratic polynomial
A complex quadratic polynomial is a quadratic polynomial whose coefficients and variable are complex numbers. Quadratic polynomials have the following
Complex_quadratic_polynomial
Quantum search algorithm
require exponentially many steps, and Grover's algorithm provides at most a quadratic speedup over the classical solution for unstructured search, this suggests
Grover's_algorithm
Continuous probability distribution
theory and statistics, the U-quadratic distribution is a continuous probability distribution defined by a unique convex quadratic function with lower limit
U-quadratic_distribution
Typesetting system
specifically for mathematical formulas. For example, the quadratic formula (which is the solution of the quadratic equation) appears as: The formula is printed in
TeX
Combinatorial optimization problem
Quadratic unconstrained binary optimization (QUBO), also known as unconstrained binary quadratic programming (UBQP), is a combinatorial optimization problem
Quadratic unconstrained binary optimization
Quadratic_unconstrained_binary_optimization
Statistical distance measure
The Mahalanobis distance is a measure of the distance between a point P {\displaystyle P} and a probability distribution D {\displaystyle D} , introduced
Mahalanobis_distance
Function in number theory
defined as ( a p ) = { 1 if a is a quadratic residue modulo p and a ≢ 0 ( mod p ) , − 1 if a is a quadratic nonresidue modulo p , 0 if a ≡ 0 (
Legendre_symbol
Function of the coefficients of a polynomial that gives information on its roots
factoring, number theory, and algebraic geometry. The discriminant of the quadratic polynomial a x 2 + b x + c {\displaystyle ax^{2}+bx+c} is b 2 − 4 a c
Discriminant
Length in a vector space
In those cases the norm is a definite quadratic form. In the split algebras the norm is an isotropic quadratic form. For any norm p : X → R {\displaystyle
Norm_(mathematics)
In forestry, quadratic mean diameter or QMD is a measure of central tendency which is considered more appropriate than arithmetic mean for characterizing
Quadratic_mean_diameter
Mathematical function defined piecewise by polynomials
type. (Note: while the polynomial piece 2t is not quadratic, the result is still called a quadratic spline. This demonstrates that the degree of a spline
Spline_(mathematics)
Product of a number by itself
be used in place of x2. The adjective which corresponds to squaring is quadratic. The square of an integer may also be called a square number or a perfect
Square_(algebra)
quadratic form Q over a field K takes values in the Brauer group Br(K). The name "Hasse–Witt" comes from Helmut Hasse and Ernst Witt. The quadratic form
Hasse invariant of a quadratic form
Hasse_invariant_of_a_quadratic_form
Sequential linear-quadratic programming (SLQP) is an iterative method for nonlinear optimization problems where objective function and constraints are
Sequential linear-quadratic programming
Sequential_linear-quadratic_programming
In mathematics, a universal quadratic form is a quadratic form over a ring that represents every element of the ring. A non-singular form over a field
Universal_quadratic_form
Number, approximately 1.618
golden ratio. The constant φ {\displaystyle \varphi } satisfies the quadratic equation φ 2 = φ + 1 {\displaystyle \textstyle \varphi ^{2}=\varphi
Golden_ratio
Quantum mechanical model
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually
Quantum_harmonic_oscillator
Algorithm for finding zeros of functions
Furthermore, for a root of multiplicity 1, the convergence is at least quadratic (see Rate of convergence) in some sufficiently small neighbourhood of
Newton's_method
Linear optimal control technique
In control theory, the linear–quadratic–Gaussian (LQG) control problem is one of the most fundamental optimal control problems, and it can also be operated
Linear–quadratic–Gaussian control
Linear–quadratic–Gaussian_control
Square root of the mean square
S x {\displaystyle \mathrm {RMS} _{x}} . The RMS is also known as the quadratic mean (denoted M 2 {\displaystyle M_{2}} ), a special case of the generalized
Root_mean_square
Mathematical Quadratic formula
finite group theory, a quadratic pair for the odd prime p, introduced by Thompson (1971), is a finite group G together with a quadratic module, a faithful
Quadratic_pair
Model in classical and quantum mechanics
models describe pointlike particles on a line or a circle with quadratic or inverse quadratic interactions between them. CMS models are named after Francesco
Calogero–Moser–Sutherland model
Calogero–Moser–Sutherland_model
Portrayal of sexual subject matter
Jennifer A. (2018). "Personal Pornography Viewing and Sexual Satisfaction: A Quadratic Analysis". Journal of Sex & Marital Therapy. 44 (3): 308–315. doi:10.1080/0092623X
Pornography
A quadratic residue code is a type of cyclic code. Examples of quadratic residue codes include the ( 7 , 4 ) {\displaystyle (7,4)} Hamming code over G
Quadratic_residue_code
Fractal curve
several variants of the Koch curve were designed, considering right angles (quadratic), other angles (Cesàro), circles and polyhedra and their extensions to
Koch_snowflake
Independent parameter describing the state of a physical system
It is often useful to specify quadratic degrees of freedom. These are degrees of freedom that contribute in a quadratic function to the energy of the
Degrees of freedom (physics and chemistry)
Degrees_of_freedom_(physics_and_chemistry)
Vector in statistics
ε {\displaystyle \varepsilon ^{T}\Lambda \varepsilon } is known as a quadratic form in ε {\displaystyle \varepsilon } . It can be shown that E [ ε
Quadratic_form_(statistics)
Study of mathematical algorithms for optimization problems
difficult than regular linear programming. Quadratic programming allows the objective function to have quadratic terms, while the feasible set must be specified
Mathematical_optimization
Result on simultaneous representation of primes by quadratic forms
mathematics, Kaplansky's theorem on quadratic forms is a result on simultaneous representation of primes by quadratic forms. It was proved in 2003 by Irving
Kaplansky's theorem on quadratic forms
Kaplansky's_theorem_on_quadratic_forms
Branch of pure mathematics
century. Gauss proved in this work the law of quadratic reciprocity and developed the theory of quadratic forms. He also introduced some basic notation
Number_theory
Type of algebras, possibly non associative
necessarily associative algebra over K together with a nondegenerate quadratic form N that satisfies N ( x y ) = N ( x ) N ( y ) {\displaystyle N(xy)=N(x)N(y)}
Composition_algebra
Two geometries based on axioms closely related to those specifying Euclidean geometry
postulate with an alternative, or consideration of quadratic forms other than the definite quadratic forms associated with metric geometry. In the former
Non-Euclidean_geometry
Formula concerning prime numbers
Euler's criterion is a formula for determining whether an integer is a quadratic residue modulo a prime. Precisely, Let p be an odd prime and a be an integer
Euler's_criterion
Procedure to solve equations of second degree
In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is a x 2 + b x + c = 0 , {\displaystyle ax^{2}+bx+c=0
Solving quadratic equations with continued fractions
Solving_quadratic_equations_with_continued_fractions
The quadratic Frobenius test (QFT) is a probabilistic primality test to determine whether a number is a probable prime. It is named after Ferdinand Georg
Quadratic_Frobenius_test
Approximation of a function by a polynomial
function, and the second-order Taylor polynomial is often referred to as the quadratic approximation. There are several versions of Taylor's theorem, some giving
Taylor's_theorem
Mathematical configuration
binary quadratic forms and other such forms. To each pair of opposite faces of a Bhargava cube one can associate an integer binary quadratic form thus
Bhargava_cube
Two quadratic forms over a number field are equivalent iff they are equivalent locally
theorem is a fundamental result in number theory which states that two quadratic forms over a number field are equivalent if and only if they are equivalent
Hasse–Minkowski_theorem
Fractal first proposed by Hermann Minkowski
create a quadratic Koch island or Minkowski island/[snow]flake: Islands Self-avoiding walk Vicsek fractal Quadratic Koch curve type 2 Quadratic Koch curve
Minkowski_sausage
Locus of the zeros of a polynomial of degree two
quadrics have dimension two, and are known as quadric surfaces. Their quadratic equations have the form m x x x 2 + m y y y 2 + m z z z 2 + 2 m x y x
Quadric
Quadratic form related to curvatures of surfaces
differential geometry, the second fundamental form (or shape tensor) is a quadratic form on the tangent plane of a smooth surface in the three-dimensional
Second_fundamental_form
Algebra based on a vector space with a quadratic form
a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure
Clifford_algebra
Term in mathematical optimization
objective function that is approximated using a model function (often a quadratic). If an adequate model of the objective function is found within the trust
Trust_region
Invariant of a quadratic form over a field of characteristic 2
In mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by Turkish mathematician Cahit Arf (1941)
Arf_invariant
Number
arithmetic Chinese remainder theorem Arithmetic functions Advanced concepts Quadratic forms Modular forms L-functions Diophantine equations Diophantine approximation
0
Spectral line splitting in electrical field
effect is either linear (proportional to the applied electric field) or quadratic with a high accuracy. The Stark effect can be observed both for emission
Stark_effect
Scalar-valued bilinear function
there exists an associated quadratic form Q : V → K defined by Q : V → K : v ↦ B(v, v). When char(K) ≠ 2, the quadratic form Q is determined by the symmetric
Bilinear_form
German polymath and scholar (1777–1855)
made numerous contributions, such as the composition law, the law of quadratic reciprocity, and proved the triangular case of the Fermat polygonal number
Carl_Friedrich_Gauss
QUADRATIC
QUADRATIC
QUADRATIC
QUADRATIC
Female
English
French pet form of Norman Germanic Ida, IDELLE means "work."
Boy/Male
Latin
Born in the city.
Surname or Lastname
English
English : from a pet form of the medieval personal name Bartholomew.German (Swabian : Bärtle): from a pet form of Bartolomäus (see Bartholomew) or Berthold. It is also found as an altered spelling of Bartel.
Boy/Male
Tamil
Delightful
Girl/Female
Indian
Clever
Girl/Female
Indian, Tamil
Beautiful Lady
Boy/Male
Tamil
Prakunj | பà¯à®°à®•à¯à®‚ஜÂ
Girl/Female
Tamil
Wins hearts, Togetherness
Girl/Female
Latin
Born of the city.
Boy/Male
Tamil
QUADRATIC
QUADRATIC
QUADRATIC
QUADRATIC
QUADRATIC
a.
Of or pertaining to a square, or to squares; resembling a quadrate, or square; square.
n.
A nonmetallic element occurring abundantly in borax. It is reduced with difficulty to the free state, when it can be obtained in several different forms; viz., as a substance of a deep olive color, in a semimetallic form, and in colorless quadratic crystals similar to the diamond in hardness and other properties. It occurs in nature also in boracite, datolite, tourmaline, and some other minerals. Atomic weight 10.9. Symbol B.
n.
An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc.
a.
Pertaining to terms of the second degree; as, a quadratic equation, in which the highest power of the unknown quantity is a square.
n.
That branch of algebra which treats of quadratic equations.
a.
Tetragonal.