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Root of an equation

2. An edible or esculent root, especially of such plants as produce a single root, as the beet, carrot, etc.; as, the root crop. 3. 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. Specifically: (a) An ancestor or progenitor; and hence, an early race; a stem. They were the roots out of which sprang two distinct people. --Locke. (b) A primitive form of speech; one of the earliest terms employed in language; a word from which other words are formed; a radix, or radical. (c) The cause or occasion by which anything is brought about; the source. ``She herself . . . is root of bounty.' --Chaucer. The love of money is a root of all kinds of evil. --1 Tim. vi. 10 (rev. Ver.) (d) (Math.) 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. (e) (Mus.) The fundamental tone of any chord; the tone from whose harmonics, or overtones, a chord is composed. --Busby. (f) The lowest place, position, or part. ``Deep to the roots of hell.' --Milton. ``The roots of the mountains.' --Southey. 4. (Astrol.) The time which to reckon in making calculations. When a root is of a birth yknowe [known]. --Chaucer. A["e]rial roots. (Bot.) (a) Small roots emitted from the stem of a plant in the open air, which, attaching themselves to the bark of trees, etc., serve to support the plant. (b) Large roots growing from the stem, etc., which descend and establish themselves in the soil. See Illust. of Mangrove. Multiple primary root (Bot.), a name given to the numerous roots emitted from the radicle in many plants, as the squash. Primary root (Bot.), the central, first-formed, main root, from which the rootlets are given off. Root and branch, every part; wholly; completely; as, to destroy an error root and branch. Root-and-branch men, radical reformers; -- a designation applied to the English Independents (1641). See Citation under Radical, n., 2. Root barnacle (Zo["o]l.), one of the Rhizocephala. Root hair (Bot.), one of the slender, hairlike fibers found on the surface of fresh roots. They are prolongations of the superficial cells of the root into minute tubes. --Gray. Root leaf (Bot.), a radical leaf. See Radical, a., 3 (b) . Root louse (Zo["o]l.), any plant louse, or aphid, which lives on the roots of plants, as the Phylloxera of the grapevine. See Phylloxera. Root of an equation (Alg.), that value which, substituted for the unknown quantity in an equation, satisfies the equation. Root of a nail (Anat.), the part of a nail which is covered by the skin. Root of a tooth (Anat.), the part of a tooth contained in the socket and consisting of one or more fangs. Secondary roots (Bot.), roots emitted from any part of the plant above the radicle. To strike root, To take root, to send forth roots; to become fixed in the earth, etc., by a root; hence, in general, to become planted, fixed, or established; to increase and spread; as, an opinion takes root. ``The bended twigs take root.' --Milton.

2. An edible or esculent root, especially of such plants as produce a single root, as the beet, carrot, etc.; as, the root crop. 3. 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. Specifically: (a) An ancestor or progenitor; and hence, an early race; a stem. They were the roots out of which sprang two distinct people. --Locke. (b) A primitive form of speech; one of the earliest terms employed in language; a word from which other words are formed; a radix, or radical. (c) The cause or occasion by which anything is brought about; the source. ``She herself . . . is root of bounty.' --Chaucer. The love of money is a root of all kinds of evil. --1 Tim. vi. 10 (rev. Ver.) (d) (Math.) 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. (e) (Mus.) The fundamental tone of any chord; the tone from whose harmonics, or overtones, a chord is composed. --Busby. (f) The lowest place, position, or part. ``Deep to the roots of hell.' --Milton. ``The roots of the mountains.' --Southey. 4. (Astrol.) The time which to reckon in making calculations. When a root is of a birth yknowe [known]. --Chaucer. A["e]rial roots. (Bot.) (a) Small roots emitted from the stem of a plant in the open air, which, attaching themselves to the bark of trees, etc., serve to support the plant. (b) Large roots growing from the stem, etc., which descend and establish themselves in the soil. See Illust. of Mangrove. Multiple primary root (Bot.), a name given to the numerous roots emitted from the radicle in many plants, as the squash. Primary root (Bot.), the central, first-formed, main root, from which the rootlets are given off. Root and branch, every part; wholly; completely; as, to destroy an error root and branch. Root-and-branch men, radical reformers; -- a designation applied to the English Independents (1641). See Citation under Radical, n., 2. Root barnacle (Zo["o]l.), one of the Rhizocephala. Root hair (Bot.), one of the slender, hairlike fibers found on the surface of fresh roots. They are prolongations of the superficial cells of the root into minute tubes. --Gray. Root leaf (Bot.), a radical leaf. See Radical, a., 3 (b) . Root louse (Zo["o]l.), any plant louse, or aphid, which lives on the roots of plants, as the Phylloxera of the grapevine. See Phylloxera. Root of an equation (Alg.), that value which, substituted for the unknown quantity in an equation, satisfies the equation. Root of a nail (Anat.), the part of a nail which is covered by the skin. Root of a tooth (Anat.), the part of a tooth contained in the socket and consisting of one or more fangs. Secondary roots (Bot.), roots emitted from any part of the plant above the radicle. To strike root, To take root, to send forth roots; to become fixed in the earth, etc., by a root; hence, in general, to become planted, fixed, or established; to increase and spread; as, an opinion takes root. ``The bended twigs take root.' --Milton.

- the equation becomes an equality. A solution of an equation is often called a root of the equation, particularly but not only for polynomial equations. The...

- of each other. A quadratic equation always has two roots, if complex roots are included; and a double root is counted for two. A quadratic equation can...

- In mathematics, an algebraic equation or polynomial equation is an equation of the form P = 0 {\displaystyle P=0} where P is a polynomial with coefficients...

- cubic 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...

- roots of the function h(x) = f(x) – g(x). Thus root-finding algorithms allow solving any equation defined by continuous functions. However, most root-finding...

- root of a number Root of unity, a complex number which is an nth root of one Root of an equation, a solution of the equation Root of a function, more...

- a_{4}=a_{3}k\ ,} then x = − k {\displaystyle \ x=-k\ } is a root of the equation. The full quartic can then be factorized this way: a 0 x 4 + a...

- models. A linear stochastic process has a unit root if 1 is a root of the process's characteristic equation. Such a process is non-stationary but does not...

- defined by a polynomial of degree four, called a quartic polynomial. A quartic equation, or equation of the fourth degree, is an equation that equates a quartic...

- an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =. The word equation and...

- of each other. A quadratic equation always has two roots, if complex roots are included; and a double root is counted for two. A quadratic equation can...

- In mathematics, an algebraic equation or polynomial equation is an equation of the form P = 0 {\displaystyle P=0} where P is a polynomial with coefficients...

- cubic 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...

- roots of the function h(x) = f(x) – g(x). Thus root-finding algorithms allow solving any equation defined by continuous functions. However, most root-finding...

- root of a number Root of unity, a complex number which is an nth root of one Root of an equation, a solution of the equation Root of a function, more...

- a_{4}=a_{3}k\ ,} then x = − k {\displaystyle \ x=-k\ } is a root of the equation. The full quartic can then be factorized this way: a 0 x 4 + a...

- models. A linear stochastic process has a unit root if 1 is a root of the process's characteristic equation. Such a process is non-stationary but does not...

- defined by a polynomial of degree four, called a quartic polynomial. A quartic equation, or equation of the fourth degree, is an equation that equates a quartic...

- an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =. The word equation and...

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