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Relationship between the rational roots of a polynomial and its extreme coefficients
algebra, the rational root theorem (or rational root test, rational zero theorem, rational zero test or p/q theorem) states a constraint on rational solutions
Rational_root_theorem
Unique positive real number which when multiplied by itself gives 2
perfect square) or irrational. The rational root theorem (or integer root theorem) may be used to show that any square root of any natural number that is not
Square_root_of_2
Relating coefficients and roots of a polynomial
rule of signs Newton's identities Gauss–Lucas theorem Properties of polynomial roots Rational root theorem Symmetric polynomial and elementary symmetric
Vieta's_formulas
Equations of degree 5 or higher cannot be solved by radicals
the resulting sextic polynomial has a rational root, which can be easily tested for using the rational root theorem. Around 1770, Joseph Louis Lagrange
Abel–Ruffini_theorem
Every polynomial has a real or complex root
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Mathematical connection between field theory and group theory
Waerden cites the polynomial f(x) = x5 − x − 1. By the rational root theorem, this has no rational zeroes. Neither does it have linear factors modulo 2
Galois_theory
p_{i}} do not have any common root. An efficient method to compute this factorization is Yun's algorithm. Rational root theorem Pan, Victor Y. (January 1997)
Polynomial_root-finding
Polynomial zeros related to linear factors
and constant term a 0 {\displaystyle a_{0}} . (See Rational root theorem.) Use the factor theorem to conclude that ( x − a ) {\displaystyle (x-a)} is
Factor_theorem
Algorithm for division of polynomials
polynomial can be obtained. For example, if the rational root theorem produces a single (rational) root of a quintic polynomial (degree five), it can be
Polynomial_long_division
Polynomial with 1 as leading coefficient
exactly the rational numbers that are also algebraic integers. This results from the rational root theorem, which asserts that, if the rational number p
Monic_polynomial
Theorem about zeros of holomorphic functions
analysis) – Limit of roots of sequence of functions Rational root theorem – Relationship between the rational roots of a polynomial and its extreme coefficients
Rouché's_theorem
(polynomials) Polynomial remainder theorem (polynomials) Primitive element theorem (field theory) Rational root theorem (algebra, polynomials) Solutions
List_of_theorems
Field theory theorem
of the rational numbers Q, since Q has characteristic 0 and therefore every finite extension over Q is separable. Using the fundamental theorem of Galois
Primitive_element_theorem
Number whose square is a given number
square root of x is rational if and only if x is a rational number that can be represented as a ratio of two perfect squares. (See square root of 2 for
Square_root
Number that is not a ratio of integers
{\displaystyle (x^{6}-2x^{3}-1)=0} . This polynomial has no rational roots, since the rational root theorem shows that the only possibilities are ±1, but x0 is
Irrational_number
Finding values for variables that make an equation true
unknown, it is possible to solve the equation for rational-valued unknowns (see Rational root theorem), and then find solutions to the Diophantine equation
Equation_solving
square roots Cube root Root of unity Constructible number Complex conjugate root theorem Algebraic element Horner scheme Rational root theorem Gauss's lemma
List_of_polynomial_topics
Counting polynomial roots in an interval
neither a nor b is a multiple root of p, then V(a) − V(b) is the number of distinct real roots of P. The proof of the theorem is as follows: when the value
Sturm's_theorem
Result in number theory, concerning irreducible polynomials
some ai, then a root of it will generate the asserted N0.) Construction of elliptic curves with large rank. Hilbert's irreducibility theorem is used as a
Hilbert's irreducibility theorem
Hilbert's_irreducibility_theorem
Arithmetic operation, inverse of nth power
the nth root of the value a. In 1629, Albert Girard proposed the fundamental theorem of algebra, but failed to produce a proof. This theorem states that
Nth_root
Topics referred to by the same term
Therapist Renal replacement therapy Randomized response technique Rational root theorem in mathematics Refugee Review Tribunal in Australia. Recommended
RRT
(Mathematical) decomposition into a product
{\displaystyle {\tfrac {3}{2}}} is a root, so there can be no other rational root. Applying the factor theorem leads finally to the factorization 2 x
Factorization
Arithmetic operation
whether nq is rational for any positive integer n and positive non-integer rational q. For example, it is not known whether the positive root of the equation
Tetration
Theorem in transcendental number theory
polynomial whose arguments are all conjugates of one another gives a rational number. The theorem is named for Ferdinand von Lindemann and Karl Weierstrass. Lindemann
Lindemann–Weierstrass_theorem
Complex number that solves a monic polynomial with integer coefficients
result of the rational root theorem for the case of a monic polynomial. Gaussian integer Eisenstein integer Root of unity Dirichlet's unit theorem Fundamental
Algebraic_integer
Ancient geometric construction problem
k\in \mathbb {Z} } , and so k must be a root of p(x); but also k must divide 2 (by the rational root theorem); that is, k = 1, 2, −1 or −2, and none of
Doubling_the_cube
Cubic polynomials defined from a monic polynomial of degree four
polynomial P(x) has a rational root (this can be determined using the rational root theorem). The resolvent cubic R3(y) has a root of the form α2, for some
Resolvent_cubic
Positive real number which when multiplied by itself gives 5
extension of the rational numbers. The Kronecker–Weber theorem therefore guarantees that the square root of five can be written as a rational linear combination
Square_root_of_5
Counting polynomial real roots based on coefficients
Pfaffian functions. Sturm's theorem – Counting polynomial roots in an interval Rational root theorem – Relationship between the rational roots of a polynomial
Descartes'_rule_of_signs
Algebraic structure with addition, multiplication, and division
fundamental theorem of algebra, C is algebraically closed, i.e., any polynomial equation with complex coefficients has a complex solution. The rational and the
Field_(mathematics)
Construction of an angle equal to one third a given angle
it has a rational root. By the rational root theorem, this root must be ±1, ±1/2, ±1/4 or ±1/8, but none of these is a root. Therefore, p(t) is
Angle_trisection
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Polynomial without nontrivial factorization
Gauss's lemma (polynomial) Rational root theorem, a method of finding whether a polynomial has a linear factor with rational coefficients Eisenstein's
Irreducible_polynomial
Number with an integer power equal to 1
the rationals is such a subfield of a cyclotomic field – this is the content of a theorem of Kronecker, usually called the Kronecker–Weber theorem on the
Root_of_unity
In mathematics, a non-algebraic number
that is not algebraic: that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients. The best-known transcendental
Transcendental_number
Type of complex number
algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the
Algebraic_number
Used to count, measure, and label
negative one (−1), rational numbers such as one half ( 1 2 ) {\displaystyle \left({\tfrac {1}{2}}\right)} , real numbers such as the square root of 2 ( 2 ) {\displaystyle
Number
Conditions for switching order of integration in calculus
Fubini's theorem gives the conditions under which a double integral can be computed as an iterated integral, i.e. by integrating in one variable at a
Fubini's_theorem
On the transcendence of a large class of numbers
immediately from the theorem: Gelfond–Schneider constant 2 2 = 2.665144142 … {\displaystyle 2^{\sqrt {2}}=2.665144142\ldots } and its square root 2 2 = 2 2 = 1
Gelfond–Schneider_theorem
Type of mathematical expression
fundamental theorem of algebra. A root of a nonzero univariate polynomial P is a value a of x such that P(a) = 0. In other words, a root of P is a solution
Polynomial
About products of primitive polynomials
R=\mathbb {Z} } , then it says a rational root of a monic polynomial over integers is an integer (cf. the rational root theorem). To see the statement, let
Gauss's_lemma_(polynomials)
Number divisible only by 1 and itself
using divisors only up to the square root. In 1640 Pierre de Fermat stated (without proof) Fermat's little theorem (later proved by Leibniz and Euler)
Prime_number
Measures the size of the ring of integers of the algebraic number field
root of the polynomial x 3 − 21 x + 28 {\displaystyle x^{3}-21x+28} or x 3 − 21 x − 35 {\displaystyle x^{3}-21x-35} , respectively. Brill's theorem:
Discriminant of an algebraic number field
Discriminant_of_an_algebraic_number_field
Mathematical theorem
Vincent's theorem—named after Alexandre Joseph Hidulphe Vincent [fr]—is a theorem that isolates the real roots of polynomials with rational coefficients
Vincent's_theorem
and lifting the result to a factorization of the primitive part. Rational root theorem B. Hartley; T.O. Hawkes (1970). Rings, modules and linear algebra
Primitive_part_and_content
traditional techniques for finding the roots of a polynomial, such as the rational root theorem and the Descartes rule of signs. Precalculus ends with an introduction
Mathematics education in the United States
Mathematics_education_in_the_United_States
Algorithms for calculating square roots
inverse square root instead. Other methods are available to compute the square root digit by digit, or using Taylor series. Rational approximations of
Square_root_algorithms
Quotient of two integers
Dyadic rational Floating point Ford circles Gaussian rational Naive height—height of a rational number in lowest term Niven's theorem Rational data type
Rational_number
Equation for radii of tangent circles
In geometry, Descartes' theorem states that for every four kissing, or mutually tangent circles, the radii of the circles satisfy a certain quadratic
Descartes'_theorem
Theorem in real analysis
derivative is zero. The theorem is named after Michel Rolle. The theorem is a special case of, and is used to prove, the mean value theorem. If a real function
Rolle's_theorem
Nonexistence of gaps in the number line
+∞. The nested interval theorem states that the intersection of all of the intervals In contains exactly one point. The rational number line does not satisfy
Completeness of the real numbers
Completeness_of_the_real_numbers
Branch of pure mathematics
rational or integer solutions are sought. After the fall of Rome, development shifted to Asia, albeit intermittently. The Chinese remainder theorem appears
Number_theory
Mathematical expression using basic operations
{\displaystyle Q(x)} , their quotient is called a rational expression or simply rational fraction. A rational expression P ( x ) Q ( x ) {\textstyle {\frac
Algebraic_expression
Continuous function on an interval takes on every value between its values at the ends
The theorem depends on, and is equivalent to, the completeness of the real numbers. The intermediate value theorem does not apply to the rational numbers
Intermediate_value_theorem
Number representing a continuous quantity
using rational coefficients only, and such that no element of B is a rational linear combination of the others. However, this existence theorem is purely
Real_number
Algebraic expansion of powers of a binomial
algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, the power ( x
Binomial_theorem
On zeros of derivatives of cubic polynomials
Mathematical Monthly describing the theorem. Bôcher's theorem for rational functions "Carlson's proof of Marden's theorem" (PDF). Kalman, Dan (2008a), "An
Marden's_theorem
Positive real number which when multiplied by itself gives 7
square root of 7. Due to the Pythagorean theorem and Legendre's three-square theorem, 7 {\displaystyle {\sqrt {7}}} is the smallest square root of a natural
Square_root_of_7
Polynomial equation, generally univariate
belong to an integral domain. If an equation P(x) = 0 of degree n has a rational root α, the associated polynomial can be factored to give the form P(X) =
Algebraic_equation
Mathematical operation
that to a matrix of integers, which can have a square root whose entries are all non-integer rational numbers, as demonstrated in some of the above examples
Square_root_of_a_matrix
paper is NP-complete. In 1999, a theorem due to Haga provided constructions used to divide the side of a square into rational fractions. In 2002, sarah-marie
Mathematics_of_paper_folding
Property of a partially ordered set
In this case, the intermediate value theorem states that f must have a root in the interval [a, b]. This theorem can be proved by considering the set
Least-upper-bound_property
Field theory result
irreducibility theorem, a field theory result described in 1829 by Niels Henrik Abel, asserts that if f(x) is a polynomial over a field F that shares a root with
Abel's_irreducibility_theorem
Number in {..., –2, –1, 0, 1, 2, ...}
integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In fact, (rational) integers are algebraic integers
Integer
Power series with rational exponents
(non-truncated) Puiseux series and proved the theorem that is now known as Puiseux's theorem or Newton–Puiseux theorem. The theorem asserts that, given an algebraic
Puiseux_series
Sufficient condition for polynomial irreducibility
the linear factor x − 1, corresponding to its obvious root 1 (which is its only rational root if p > 2): x p − 1 x − 1 = x p − 1 + x p − 2 + ⋯ + x +
Eisenstein's_criterion
Describes statistically the splitting of primes in a given Galois extension of Q
the cyclotomic extensions, obtained from the field of rational numbers by adjoining a primitive root of unity of a given order. For example, the ordinary
Chebotarev_density_theorem
Every finite abelian extension of Q is contained within some cyclotomic field
adjoining a root of unity to the rational numbers. For a given abelian extension K of Q there is a minimal cyclotomic field that contains it. The theorem allows
Kronecker–Weber_theorem
Economic theorem
The Sonnenschein–Mantel–Debreu theorem is an important result in general equilibrium economics, proved by Gérard Debreu, Rolf Mantel [es], and Hugo F
Sonnenschein–Mantel–Debreu theorem
Sonnenschein–Mantel–Debreu_theorem
Unit-distance-preserving maps are isometries
rediscovered by other authors and re-proved in multiple ways. Analogous theorems for rational subsets of Euclidean spaces, or for non-Euclidean geometry, are
Beckman–Quarles_theorem
Number represented as a0+1/(a1+1/...)
approximate with rational numbers. Hurwitz's theorem states that any irrational number k can be approximated by infinitely many rational m/n with | k
Simple_continued_fraction
Every symmetric convex set in R^n with volume > 2^n contains a non-zero integer point
Minkowski's theorem can be used to prove Dirichlet's theorem on simultaneous rational approximation. Another application of Minkowski's theorem is the result
Minkowski's_theorem
Representation of modular integers by "small" fractions
integer greater than the square root of m, but the general form is sometimes useful, and makes the uniqueness theorem (below) easier to state. The first
Thue's_lemma
Algebraic structure where all polynomials have roots
polynomial with coefficients in F has a root in F. In other words, a field is algebraically closed if the fundamental theorem of algebra holds for it. For example
Algebraically_closed_field
Product of an integer with itself
integer root is the only divisor that pairs up with itself to yield the square number, while other divisors come in pairs. Lagrange's four-square theorem states
Square_number
Correspondence between subfields and subgroups
In mathematics, the fundamental theorem of Galois theory is a result that describes the structure of certain types of field extensions in relation to
Fundamental theorem of Galois theory
Fundamental_theorem_of_Galois_theory
Theorem in dimensional analysis
Buckingham π theorem is a key theorem in dimensional analysis. It is a formalisation of Rayleigh's method of dimensional analysis. Loosely, the theorem states
Buckingham_pi_theorem
Methods for locating real roots of a polynomial
section). The first complete real-root isolation algorithm results from Sturm's theorem (1829). However, when real-root-isolation algorithms began to be
Real-root_isolation
Local-global result for when an element in a number field is an nth power
In algebraic number theory, the Grunwald–Wang theorem is a local-global principle stating that—except in some precisely defined cases—an element x in
Grunwald–Wang_theorem
Polynomial equation of degree 3
Abel–Ruffini theorem.) geometrically: using Omar Khayyam's method. trigonometrically numerical approximations of the roots can be found using root-finding
Cubic_equation
Curve defined as zeros of polynomials
curve Rational normal curve Riemann–Roch theorem for algebraic curves Weber's theorem (Algebraic curves) Riemann–Hurwitz formula Riemann–Roch theorem for
Algebraic_curve
Integers have unique prime factorizations
mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
Algebraic surface defined by a cubic polynomial
that they are all rational, as shown by Alfred Clebsch in 1866. That is, there is a one-to-one correspondence defined by rational functions between the
Cubic_surface
Number system extending the rational numbers
which is itself based on the following theorem: If r = n d {\displaystyle r={\tfrac {n}{d}}} is a rational number such that 0 ≤ r < 1 , {\displaystyle
P-adic_number
Branch of mathematics that studies dynamical systems
theorem holds are conservative systems; thus all ergodic systems are conservative. More precise information is provided by various ergodic theorems which
Ergodic_theory
Mathematical concept
the solution to some quadratic equation with rational coefficients which is irreducible over the rational numbers. Since fractions in the coefficients
Quadratic_irrational_number
Finite extension of the rationals
a number field obtained by adjoining the square root of d {\displaystyle d} to the field of rational numbers. Arithmetic operations in this field are
Algebraic_number_field
Gives information about the Galois module structure of class groups of cyclotomic fields
In mathematics, Stickelberger's theorem is a result of algebraic number theory, which gives some information about the Galois module structure of class
Stickelberger's_theorem
Number with a real and an imaginary part
field of rational numbers Q {\displaystyle \mathbb {Q} } (the polynomial x2 − 2 does not have a rational root, because √2 is not a rational number) nor
Complex_number
Branch of number theory
Hahn–Banach theorem are different. Ostrowski's theorem, due to Alexander Ostrowski (1916), states that every non-trivial absolute value on the rational numbers
P-adic_analysis
Algorithm for finding zeros of functions
method Euler method Fast inverse square root Fisher scoring Gradient descent Integer square root Kantorovich theorem Laguerre's method Methods of computing
Newton's_method
Two to the power of the square root of two
follows: either 2 2 {\displaystyle {\sqrt {2}}^{\sqrt {2}}} is a rational which proves the theorem, or it is irrational (as it turns out to be) and then ( 2
Gelfond–Schneider_constant
Construction in transcendental number theory
x close to zero. If e is a rational number then by letting x = 1 in the above formula we see that R(1) is also a rational number. However, Fourier proved
Auxiliary_function
Mathematical arithmetic dynamics function
for every n {\displaystyle n} . In 1992, Stoll proved the following theorem: Theorem: the arboreal representation ρ f , 0 {\displaystyle \rho _{f,0}} is
Arboreal Galois representation
Arboreal_Galois_representation
Sequence of points that get progressively closer to each other
consists of rational numbers (1, 3/2, 17/12,...), which is clear from the definition; however it converges to the irrational square root of 2, see Babylonian
Cauchy_sequence
Field extension of the rational numbers by a primitive root of unity
field obtained by adjoining a complex root of unity to Q {\displaystyle \mathbb {Q} } , the field of rational numbers. Cyclotomic fields played a crucial
Cyclotomic_field
Mathematical proof technique using contradiction
Fermat. The Mordell–Weil theorem was at the start of what later became a very extensive theory. The proof that the square root of 2 (√2) is irrational
Proof_by_infinite_descent
Algorithm in computational number theory
polynomial-time algorithms for factorizing polynomials with rational coefficients, for finding simultaneous rational approximations to real numbers, and for solving
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
Lenstra–Lenstra–Lovász_lattice_basis_reduction_algorithm
Cubic equation unsolvable in real radicals
6x − 1 = 0, which fails the rational root test as none of the rational numbers suggested by the theorem is actually a root. Therefore, the minimal polynomial
Casus_irreducibilis
Polynomial function of degree 5
solutions of general quintic equations over the rationals; this statement is known as the Abel–Ruffini theorem, first asserted in 1799 and completely proven
Quintic_function
RATIONAL ROOT-THEOREM
RATIONAL ROOT-THEOREM
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Animated; Rational
Surname or Lastname
English
English : patronymic from Root 1.
Boy/Male
Hindu
Rational
Boy/Male
Hindu
Rational
Boy/Male
Muslim
Spirit, Soul, Good behaviour, Purity
Boy/Male
Egyptian
Root.
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.
Boy/Male
Hindu, Indian, Tamil
Revolving; Pearl
Boy/Male
Tamil
Rational
Male
Chinese
a root.
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.
Girl/Female
Hindu, Indian
Rational
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.
Boy/Male
Indian, Sanskrit
Beginning; Root
Boy/Male
Tamil
Rational
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
Hindu, Indian, Indonesian, Kenyan
Root
Boy/Male
Gujarati, Hindu, Indian
Lord of Pleasure
Girl/Female
Hindu, Indian
Rational
Surname or Lastname
English
English : variant spelling of Foote.
RATIONAL ROOT-THEOREM
RATIONAL ROOT-THEOREM
Girl/Female
Hindu, Indian
A Divine; Unique Soul
Girl/Female
Indian
Praise of Allah swt
Girl/Female
Tamil
Auspicious, Fragrant
Girl/Female
Assamese, Bengali, Hindu, Indian, Kannada, Marathi, Sanskrit, Telugu
The Capital
Boy/Male
Muslim
Name of third dynsaty of Persian kings
Boy/Male
Hindu, Indian, Tamil
Younger
Boy/Male
American, Australian, Chinese, Christian, French, German, Jamaican, Teutonic
Famous Warrior; Famous in Battle; People's Army
Girl/Female
Arabic, Assamese, Australian, Hindu, Indian, Marathi, Muslim, Sindhi
Mirror; Reflection
Girl/Female
Arabic, Muslim, Sindhi
Foreign; Strange; Daughter of Salim Bin Ahmad At-tajir had this Name
Girl/Female
Tamil
Vasudhara | வஸà¯à®¤à®¾à®°à®¾
Earth
RATIONAL ROOT-THEOREM
RATIONAL ROOT-THEOREM
RATIONAL ROOT-THEOREM
RATIONAL ROOT-THEOREM
RATIONAL ROOT-THEOREM
a.
Relatively small; inconsiderable; insignificant; as, a fractional part of the population.
n.
An edible or esculent root, especially of such plants as produce a single root, as the beet, carrot, etc.; as, the root crop.
a.
Of or pertaining to a nation; common to a whole people or race; public; general; as, a national government, language, dress, custom, calamity, etc.
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.
a.
Of or pertaining to fractions or a fraction; constituting a fraction; as, fractional numbers.
a.
Given to foolish or visionary expectations; whimsical; fanciful; as, a notional man.
v. t.
To cover or dress with soot; to smut with, or as with, soot; as, to soot land.
a.
Involving an option; depending on the exercise of an option; left to one's discretion or choice; not compulsory; as, optional studies; it is optional with you to go or stay.
v. i.
To search or root in the ground, as a swine.
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 tear up by the root; to eradicate; to extirpate; -- with up, out, or away.
a.
Agreeable to reason; not absurd, preposterous, extravagant, foolish, fanciful, or the like; wise; judicious; as, rational conduct; a rational man.
v. i.
To fix the root; to enter the earth, as roots; to take root and begin to grow.
a.
Not rational; void of reason or understanding; as, brutes are irrational animals.
n.
A rational being.
a.
Full of roots; as, rooty ground.
adv.
In a rational manner.
v. t.
To supply with rations, as a regiment.
a.
Feeding on roots; root-eating.