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Finding the roots of polynomials is a long-standing problem that has been extensively studied throughout the history and substantially influenced the development
Polynomial_root-finding
Algorithms for zeros of functions
behavior of general root-finding algorithms is studied in numerical analysis. However, for polynomials specifically, the study of root-finding algorithms belongs
Root-finding_algorithm
Algorithm for polynomial evaluation
x ) {\displaystyle p(x)} . Evaluating a polynomial and its derivative at a point is useful for root-finding via Newton's method. Horner's paper, titled
Horner's_method
Point where function's value is zero
may provide all roots or all real roots; see Polynomial root-finding and Real-root isolation. Some polynomial, including all those of degree no greater than
Zero_of_a_function
Relationship between the rational roots of a polynomial and its extreme coefficients
rational root theorem is a special case (for a single linear factor) of Gauss's lemma on the factorization of polynomials. The integral root theorem is
Rational_root_theorem
Polynomial root-finding algorithm
Daniel Bernoulli, is a root-finding algorithm which calculates the root of largest absolute value of a univariate polynomial. The method works under
Bernoulli's_method
Geometry of the location of polynomial roots
distance between two roots. Such bounds are widely used for root-finding algorithms for polynomials, either for tuning them, or for computing their computational
Geometrical properties of polynomial roots
Geometrical_properties_of_polynomial_roots
Polynomial root-finding algorithm
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
Laguerre's_method
Type of mathematical expression
(see Root-finding algorithm). For polynomials with more than one indeterminate, the combinations of values for the variables for which the polynomial function
Polynomial
Root-finding algorithm for polynomials
The Jenkins–Traub algorithm for polynomial zeros is a fast globally convergent iterative polynomial root-finding method published in 1970 by Michael A
Jenkins–Traub_algorithm
Swiss mathematician and physicist (1700–1782)
of translation and motion of rotation. In 1729, he published a polynomial root-finding algorithm which became known as Bernoulli's method. His chief work
Daniel_Bernoulli
Polynomial equation, generally univariate
equation (see Root-finding algorithm) and of the common solutions of several multivariate polynomial equations (see System of polynomial equations). The
Algebraic_equation
Algorithms for calculating square roots
interval, or finding a better functional approximation to f ( x ) {\displaystyle f(x)} . The latter usually means using a higher order polynomial in the approximation
Square_root_algorithms
Algorithm for finding zeros of functions
as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots
Newton's_method
Algorithm used for frequency estimation and radio direction finding
autoregressive coefficients, whose zeros can be found analytically or with polynomial root finding algorithms. In contrast, MUSIC assumes that several such functions
MUSIC_(algorithm)
Algorithm for finding a zero of a function
bisection method into efficient algorithms for finding all real roots of a polynomial; see Real-root isolation. The method is applicable for numerically
Bisection_method
Formula that provides the solutions to a quadratic equation
gives only one root, even when both roots are positive. The Indian mathematician Brahmagupta included a generic method for finding one root of a quadratic
Quadratic_formula
Polynomial function of degree 5
approximations of quintics roots can be computed with root-finding algorithms for polynomials. Although some quintics may be solved in terms of radicals
Quintic_function
Polynomial in numerical analysis
Wilkinson's polynomial is a specific polynomial which was used by James H. Wilkinson in 1963 to illustrate a difficulty when finding the roots of a polynomial: the
Wilkinson's_polynomial
Function's sensitivity to argument change
difficulties of numerous computational problems, for example, polynomial root finding or computing eigenvalues. The condition number of f {\displaystyle
Condition_number
Computational method
every polynomial with complex coefficients has complex roots, implies that a polynomial with integer coefficients can be factored (with root-finding algorithms)
Factorization_of_polynomials
Number whose square is a given number
} Given any polynomial p, a root of p is a number y such that p(y) = 0. For example, the nth roots of x are the roots of the polynomial (in y) y n −
Square_root
Arithmetic operation, inverse of nth power
every single-variable polynomial of degree n has n roots. Further, a polynomial with complex coefficients has at least one complex root. Equivalently, the
Nth_root
Every polynomial has a real or complex root
non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Algorithm for division of polynomials
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version
Polynomial_long_division
Root-finding algorithm for polynomials
analysis, Bairstow's method is an efficient algorithm for finding the roots of a real polynomial of arbitrary degree. The algorithm first appeared in the
Bairstow's_method
Factorisation algorithm
x_{0}} is a root of f over Q and can be found easily. More generally, we can find a polynomial f ( x ) {\displaystyle f(x)} with the same root x 0 {\displaystyle
Coppersmith_method
Polynomial equation of degree two
c to be a root of the polynomial x2 + x + c, an element of the splitting field of that polynomial. One verifies that R(c) + 1 is also a root. In terms
Quadratic_equation
(Mathematical) decomposition into a product
In this case, the factorization can be done with root-finding algorithms. The case of polynomials with integer coefficients is fundamental for computer
Factorization
Algebraic structure
especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates (traditionally
Polynomial_ring
Cubic polynomials defined from a monic polynomial of degree four
of P(x) is useful for finding the roots of P(x) itself. Hence the name “resolvent cubic”. The polynomial P(x) has a multiple root if and only if its resolvent
Resolvent_cubic
Function in algebraic graph theory
The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a
Chromatic_polynomial
Mathematical concept in polynomial theory
resultant of two polynomials is a polynomial expression of their coefficients that is equal to zero if and only if the polynomials have a common root (possibly
Resultant
Concepts from linear algebra
found by factoring the characteristic polynomial, or numerically by root finding. The characteristic polynomial can be factored into the product of n
Eigenvalues_and_eigenvectors
Greatest common divisor of polynomials
square-free factorization reduces root-finding of a polynomial with multiple roots to root-finding of several square-free polynomials of lower degree. The square-free
Polynomial greatest common divisor
Polynomial_greatest_common_divisor
Modular arithmetic concept
Finding primitive roots modulo p is also equivalent to finding the roots of the (p − 1)st cyclotomic polynomial modulo p. The least primitive root gp
Primitive_root_modulo_n
Type of analog linear filter in electronics
(polynomial to be factored) R = j 5.0771344 (the positive imaginary root for the above polynomial) For even order filters, use the positive real root
Bessel_filter
Polynomial division computation method
needs the quotient, is the factorization of a polynomial p ( x ) {\displaystyle p(x)} for which one knows a root r: The remainder of the Euclidean division
Ruffini's_rule
Root-finding algorithm
the ITP method (Interpolate Truncate and Project method) is the first root-finding algorithm that achieves the superlinear convergence of the secant method
ITP_method
Number whose cube is a given number
method for finding the cube root of numbers having many digits in the Aryabhatiya (section 2.5). Methods of computing square roots List of polynomial topics
Cube_root
Russian mathematician (born 1957)
Shparlinski, Igor E. (2015). "Character sums and deterministic polynomial root finding in finite fields". Mathematics of Computation. 84 (296): 2969–2977
Sergei_Konyagin
Polynomial without nontrivial factorization
an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property of
Irreducible_polynomial
Algorithm for finding polynomial roots
Dandelin–Lobachesky–Graeffe method is an algorithm for finding all of the roots of a polynomial. It was developed independently by Germinal Pierre Dandelin
Graeffe's_method
Root-finding algorithm for polynomials
independently by Durand in 1960 and Kerner in 1966, is a root-finding algorithm for solving polynomial equations. In other words, the method can be used to
Durand–Kerner_method
Mathematical expression using basic operations
{1-x^{2}}{1+x^{2}}}}} An algebraic equation is an equation involving polynomials, for which algebraic expressions may be solutions. If the set of constants
Algebraic_expression
Mathematical test in control system theory
c\neq 0} (to avoid a root in zero so that we can use the Routh–Hurwitz theorem). First, we have to calculate the real polynomials P 0 ( y ) {\displaystyle
Routh–Hurwitz stability criterion
Routh–Hurwitz_stability_criterion
Root-finding algorithm for polynomials
W. Ehrlich, is a root-finding algorithm developed in 1967 for simultaneous approximation of all the roots of a univariate polynomial. This method converges
Aberth_method
Counting polynomial roots in an interval
exactly one root. This yields the oldest real-root isolation algorithm, and arbitrary-precision root-finding algorithm for univariate polynomials. For computing
Sturm's_theorem
In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition
Factorization of polynomials over finite fields
Factorization_of_polynomials_over_finite_fields
In mathematics, a non-algebraic number
real or complex number that is not algebraic: that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients. The
Transcendental_number
Polynomial function of degree 4
} where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial. A quartic equation, or equation of the fourth degree
Quartic_function
Polynomial equation of degree 3
equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). All of the roots of the cubic equation
Cubic_equation
Graphical method for the real roots of a polynomial
mathematics, Lill's method is a visual method of finding the real roots of a univariate polynomial of any degree. It was developed by Austrian engineer
Lill's_method
Methods for locating real roots of a polynomial
root of the polynomial, and, together, contain all the real roots of the polynomial. Real-root isolation is useful because usual root-finding algorithms
Real-root_isolation
Integer factorization algorithm
therefore the ceiling of the square root of N {\displaystyle N} is 124. Since N {\displaystyle N} is small, the basic polynomial Y ( X ) = ( X + 124 ) 2 − 15347
Quadratic_sieve
Polynomial sequence
In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets
Hermite_polynomials
Polynomial equation of degree 4
remove any requirement for trial by using a root of the same resolvent polynomial for factoring; if w is any root of (3), and if F 1 = x 2 + w x + 1 2 w 2
Quartic_equation
Algorithm to smooth data points
Following the aforementioned finding by Nikitas and Pappa-Louisi in two-dimensional cases, usage of the following form of the polynomial is recommended in multidimensional
Savitzky–Golay_filter
Method in number theory
Berlekamp's root finding algorithm, also called the Berlekamp–Rabin algorithm, is the probabilistic method of finding roots of polynomials over the field
Berlekamp–Rabin_algorithm
Invariant of polynomial roots
G is a polynomial whose coefficients depend polynomially on the coefficients of a given polynomial p and has, roughly speaking, a rational root if and
Resolvent_(Galois_theory)
Method for solving quadratic equations
quadratic polynomial with no linear term. By subsequently isolating ( x − h ) 2 {\displaystyle \textstyle (x-h)^{2}} and taking the square root, a quadratic
Completing_the_square
American computer scientist
Society. Retrieved 15 November 2021. Binner, David (6 March 2008). "Polynomial Root-finding with the Jenkins-Traub Algorithm". Math ∞ Blog. Retrieved 4 April
Joseph_F._Traub
Number with a real and an imaginary part
rational numbers Q {\displaystyle \mathbb {Q} } (the polynomial x2 − 2 does not have a rational root, because √2 is not a rational number) nor the real
Complex_number
Mathematical construct in computer algebra
is only theoretical, because it implies GCD computation and root-finding of polynomials with approximate coefficients, which are not practicable because
Gröbner_basis
Polynomial function of degree two
function, is a quadratic polynomial, a polynomial of degree two. In elementary mathematics a polynomial and its associated polynomial function are rarely distinguished
Quadratic_function
Error-correcting codes
received polynomial r(x) reproduces the original codeword s. The Berlekamp–Massey algorithm is an alternate iterative procedure for finding the error
Reed–Solomon_error_correction
Polynomial zeros related to linear factors
f(a)=0} (that is, a {\displaystyle a} is a root of the polynomial). The theorem is a special case of the polynomial remainder theorem. The theorem results
Factor_theorem
Software for approximating the roots of a polynomial with arbitrarily high precision
portal Mathematics portal Polynomial root-finding algorithms "Design, Analysis, and Implementation of a Multiprecision Polynomial Rootfinder" by D. A. Bini
MPSolve
Measure of distance between atoms of superimposed proteins
In bioinformatics, the root mean square deviation of atomic positions, or simply root mean square deviation (RMSD), is the measure of the average distance
Root mean square deviation of atomic positions
Root_mean_square_deviation_of_atomic_positions
Transformation of a polynomial induced by a transformation of its roots
reduce any question on the roots of a polynomial, such as root-finding, to a similar question on a simpler polynomial, which is monic and does not have a
Polynomial_transformation
Quantum algorithm for integer factorization
N {\displaystyle N} , Shor's algorithm runs in polynomial time, meaning the time taken is polynomial in log N {\displaystyle \log N} . It takes quantum
Shor's_algorithm
Mathematical formula expressing equality
equation (see Root finding of polynomials) and of the common solutions of several multivariate polynomial equations (see System of polynomial equations)
Equation
Result in modular arithmetic
stating that if a univariate polynomial has a simple root modulo a prime number p, then this root can be lifted to a unique root modulo any higher power of
Hensel's_lemma
Root-finding algorithm
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's_method
Quadratic polynomial
complex quadratic polynomial is a quadratic polynomial whose coefficients and variable are complex numbers. Quadratic polynomials have the following
Complex_quadratic_polynomial
Cryptographic algorithm created by Adi Shamir
specifically that k {\displaystyle k} points on the polynomial uniquely determines a polynomial of degree less than or equal to k − 1 {\displaystyle
Shamir's_secret_sharing
Generalisation of Fourier transform to any ring
_{i}p_{i}^{e_{i}}} , then one may find an n t h {\textstyle n^{th}} root of unity mod m by finding primitive n t h {\textstyle n^{th}} roots of unity g i {\displaystyle
Discrete Fourier transform over a ring
Discrete_Fourier_transform_over_a_ring
Study of polynomial equations
have led to the development of algebraic geometry. Root-finding algorithm Properties of polynomial roots Quintic function https://www.britannica
Theory_of_equations
Mathematical term; type of polynomial transformation
that takes a root to some rational function applied to that root. For a generic n t h {\displaystyle n^{th}} degree reducible monic polynomial equation f
Tschirnhaus_transformation
Class of problems solvable in polynomial time
solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time. Cobham's thesis holds that P is the class of
P_(complexity)
Computation modulo a fixed integer
exponentiation) p(a) ≡ p(b) (mod m), for any polynomial p(x) with integer coefficients (compatibility with polynomial evaluation) If a ≡ b (mod m), then it is
Modular_arithmetic
Factorization algorithm
n=a_{d}m^{d}+\cdots +a_{1}m+a_{0}} , which in turn means that m is a root of the polynomial f ( x ) = a d x d + ⋯ + a 1 x + a 0 {\textstyle f(x)=a_{d}x^{d}+\cdots
General_number_field_sieve
Task of computing complete subgraphs
can be proven to be a super-polynomial function of the number of vertices and the clique size, exponential in the cube root of the number of vertices.
Clique_problem
Root-finding algorithm
(named after Derrick Henry Lehmer and Issai Schur) is a root-finding algorithm for complex polynomials, extending the idea of enclosing roots like in the one-dimensional
Lehmer–Schur_algorithm
Algorithm for finding roots of a function
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
Muller's_method
Signal processing filter
_{c}} is found to be 1.2186824. The polynomial scaled inversion function may be performed by translating each root, s, to Ω c / s {\displaystyle \Omega
Elliptic_filter
System where changes of output are not proportional to changes of input
methods for polynomials allow finding all roots or the real roots; see real-root isolation. Solving systems of polynomial equations, that is finding the common
Nonlinear_system
Error correction code
any polynomial that is a multiple of the generator polynomial is a valid BCH codeword, BCH encoding is merely the process of finding some polynomial that
BCH_code
Branch of mathematics
As a study of systems of polynomial equations in several variables, the subject of algebraic geometry begins with finding specific solutions via equation
Algebraic_geometry
Finding values for variables that make an equation true
A solution of an equation is often called a root of the equation, particularly but not only for polynomial equations. The set of all solutions of an equation
Equation_solving
Ancient geometric construction problem
cases, both the x- and y-coordinates of the newly defined point satisfy a polynomial of degree no higher than a quadratic, with coefficients that are additions
Doubling_the_cube
Root-finding algorithm for polynomials
is a root-finding algorithm extending the idea of enclosing roots, as in the one-dimensional bisection method, to find the roots of a polynomial inside
Wilf's global bisection algorithm
Wilf's_global_bisection_algorithm
Probabilistic primality test
existence of an Euclidean division for polynomials). Here follows a more elementary proof. Suppose that x is a square root of 1 modulo n. Then: ( x − 1 ) (
Miller–Rabin_primality_test
Algorithm for computing greatest common divisors
such polynomials. The Gaussian integers are complex numbers of the form α = u + vi, where u and v are ordinary integers and i is the square root of negative
Euclidean_algorithm
Roots of multiple multivariate polynomials
of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in
System of polynomial equations
System_of_polynomial_equations
Used to count, measure, and label
(1872). A transcendental number is a numerical value that is not the root of a polynomial with integer coefficients. This means it is not algebraic and thus
Number
Class of mathematical root-finding algorithm
specifically in numerical analysis, Householder's methods are a class of root-finding algorithms that are used for functions of one real variable with continuous
Householder's_method
Amount left over after computation
approach to finding remainders when dividing polynomials. Identify the polynomial P(x) and the linear divisor x-a. Evaluate P(a), where a is the root of the
Remainder
orthogonal lattice basis in polynomial time Modular square root: computing square roots modulo a prime number Berlekamp's root finding algorithm Cipolla's algorithm
List_of_algorithms
Square matrices satisfy their characteristic equation
integers) satisfies its own characteristic equation. The characteristic polynomial of an n × n {\displaystyle n\times n} matrix A is defined as p A ( λ )
Cayley–Hamilton_theorem
POLYNOMIAL ROOT-FINDING
POLYNOMIAL ROOT-FINDING
Surname or Lastname
English
English : nickname for a cheerful person, from Middle English rote ‘glad’ (Old English rÅt).English : metonymic occupational name for a player on the rote, an early medieval stringed instrument (Middle English, Old French rote, of uncertain origin but apparently ultimately akin to Welsh crwth).Dutch : topographic name for someone who lived by a retting place (Dutch root, a derivative of ro(o)ten ‘to ret’, akin to modern English rot), a place where flax is soaked in tubs of water until the stems rot to release the linen fibers.
Girl/Female
Hindu
Look, Blessed with beauty, Shape, Beauty
Surname or Lastname
English
English : nickname from the bird (Old English hrÅc), most likely given to a person with very dark hair or a dark complexion or to someone with a raucous voice.English : some early examples, such as Robert of ye Rook (London 1318) and Henry del Rook (Staffordshire 1332), point clearly to a local name of some kind. The first of these could be from a house sign, the second may be a variant of Rock 1.German : from a short form of a Germanic personal name formed with hrok, of uncertain origin; perhaps a cognate of 1 or from Middle High German rÅhen ‘to cry or yell (in battle)’ or Old High German ruoh ‘intent’.Perhaps an altered spelling of German Ruck.
Surname or Lastname
English
English : variant of Rolfe.German : from Ruffo, a short form of a personal name formed with hrÅd ‘renown’, ‘victory’.Probably an Americanized spelling of German Ruf and Ruff.
Boy/Male
Indian
Spirit, Soul, Good behaviour, Purity
Surname or Lastname
English (now chiefly East Anglia)
English (now chiefly East Anglia) : probably a topographic name for someone who lived by a patch of rough ground, from a hypothetical Old English word rÅ«(we)t or rÅ«het, derivatives of rÅ«h ‘rough’, ‘overgrown’. Compare Rauch. There are places called Ruffet(t) in Surrey and Sussex which are thought to have this origin.German : Swabian variant of Roth 1.Probably an Americanized spelling of German Rauth.Indian (northern states) : Hindu (Rajput, Jat, Maratha) and Sikh name meaning ‘prince’, from Sanskrit rÄjaputra (from rÄja ‘king’ + putra ‘son’). In India this is a variant of a name more commonly spelled Ravat or Raut. The Jats have a clan called Ravat.
Surname or Lastname
English
English : variant spelling of Foote.
Boy/Male
Hindu, Indian, Indonesian, Kenyan
Root
Boy/Male
Indian, Sanskrit
Beginning; Root
Surname or Lastname
Dutch
Dutch : from a short form of the Germanic personal name Robrecht.Altered spelling of German Rupp.English : variant spelling of Roope.
Boy/Male
American, British, English
Raven
Male
Chinese
a root.
Boy/Male
Dutch
Large.
Boy/Male
Egyptian
Root.
Girl/Female
British, Dutch, English, French, German, Netherlands
Rose
Surname or Lastname
English
English : metonymic occupational name for a maker or seller of boots, from Middle English, Old French bote (of unknown origin).Dutch and North German : metonymic occupational name for a boatman, from Dutch boot ‘boat’.
Boy/Male
Muslim
Spirit, Soul, Good behaviour, Purity
Surname or Lastname
Dutch (also de Roos) and Swiss German
Dutch (also de Roos) and Swiss German : habitational name for someone living at a house distinguished by the sign of a rose.Dutch (also de Roos) : metonymic occupational name for someone who grew roses, from roos ‘rose’.Dutch : from the female personal name Rosa (Latin rosa ‘rose’).Dutch : nickname from roos ‘erysipelas’, an infection which causes reddening of the skin and scalp, applied presumably to someone with a ruddy complexion.Swiss German : from a personal name formed with hrÅd ‘renown’.Swedish and Danish (of German origin) : as 1.Swedish : variant of Ros.English and Scottish : variant of Ross 2.
Surname or Lastname
English
English : patronymic from Root 1.
Girl/Female
Indian
Soul
POLYNOMIAL ROOT-FINDING
POLYNOMIAL ROOT-FINDING
Boy/Male
American, Australian, Chinese, Christian, Gaelic, Latin, Scottish
Dove; Similar to Malcolm; Servant or Disciple of Columba; Bald Dove
Boy/Male
Arabic, Muslim, Pashtun
Playing with Flowers
Girl/Female
Spanish
Religious holiday.
Girl/Female
Hindu
In Hindi Yug, Earth, Muse (Celebrity Name: Amir Khan)
Girl/Female
Indian
Student of Hadith
Boy/Male
Hindu, Indian, Kannada, Marathi, Oriya, Telugu, Traditional
Divine Body
Girl/Female
Australian, Slavic
Born at Christmas
Girl/Female
Indian
Tall and high, Bright
Biblical
put; who puts; fixed
Boy/Male
Hindu, Indian, Traditional
Light
POLYNOMIAL ROOT-FINDING
POLYNOMIAL ROOT-FINDING
POLYNOMIAL ROOT-FINDING
POLYNOMIAL ROOT-FINDING
POLYNOMIAL ROOT-FINDING
a.
Containing many names or terms; multinominal; as, the polynomial theorem.
a.
Having roots, or possessing a well-developed root.
n. & a.
Same as Polynomial.
v. i.
To occupy a room or rooms; to lodge; as, they arranged to room together.
n.
That factor of a quantity which when multiplied into itself will produce that quantity; thus, 3 is a root of 9, because 3 multiplied into itself produces 9; 3 is the cube root of 27.
v. t.
To cover with a roof.
a.
Consisting of two or more words; having names consisting of two or more words; as, a polynomial name; polynomial nomenclature.
n.
That which resembles a root in position or function, esp. as a source of nourishment or support; that from which anything proceeds as if by growth or development; as, the root of a tooth, a nail, a cancer, and the like.
n.
An edible or esculent root, especially of such plants as produce a single root, as the beet, carrot, etc.; as, the root crop.
v. i.
To fix the root; to enter the earth, as roots; to take root and begin to grow.
n.
That which corresponds to the foot of a man or animal; as, the foot of a table; the foot of a stocking.
v. t.
To cover or dress with soot; to smut with, or as with, soot; as, to soot land.
a.
Full of roots; as, rooty ground.
a.
Feeding on roots; root-eating.
n.
A polynomial name or term.
n.
The underground portion of a plant, whether a true root or a tuber, a bulb or rootstock, as in the potato, the onion, or the sweet flag.
v. t.
To turn up or to dig out with the snout; as, the swine roots the earth.
v. t.
To tear up by the root; to eradicate; to extirpate; -- with up, out, or away.
v. i.
To search or root in the ground, as a swine.