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Topic: Positive root

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	Square root - Wikipedia, the free encyclopedia
		In mathematics, a square root of a number x is a number whose square (the result of multiplying the number by itself) is x.
		Per the fundamental theorem of algebra, there are two solutions to the equation defining the square roots of any number (although these roots may not be distinct, as in the square root of zero).
		Square roots of non-perfect squares are always irrational numbers, i.e., numbers not expressible as a ratio of two integers.
	en.wikipedia.org /wiki/Square_root (1676 words)

	Root system - Wikipedia, the free encyclopedia
		In general, irreducible root systems are specified by a family (indicated by a letter A to G) and the rank (indicated by a subscript).
		The Dynkin diagram can be extracted from the root system by choosing a base, that is a subset Δ of Φ which is a basis of V with the special property that every vector in Φ when written in the basis Δ has either all coefficients ≥0 or else all ≤0.
		Given two root systems with the same Dynkin diagram, we can match up roots, starting with the roots in the base, and show that the systems are in fact the same.
	en.wikipedia.org /wiki/Root_system (1250 words)

	Principal square root of positive real number
		The positive square root of a positive real number is called a principal square root.
		In common usage, the square root of a positive real number is taken as the principal square root.
		This is why in school, the square root of, say, 4 is taken as +2.
	www.mathpath.org /concepts/principal.square.root.htm (285 words)

	PlanetMath: positive root
		Roots which are not positive are called negative.
		is positive, exactly half the roots must be positive.
		This is version 5 of positive root, born on 2002-12-04, modified 2004-04-13.
	planetmath.org /encyclopedia/PositiveRoot.html (73 words)

	xabc
		It is clear that we will always obtain two real roots (one positive and one negative) for any value of b.
		Both roots will be negative for 0 < c < 4, one root will be negative and one 0 for c = 0, and one root will be negative and one positive when c < 0.
		For a = 0, the equation is linear with a negative root.
	jwilson.coe.uga.edu /EMT668/EMAT6680.F99/Wise/writeup3/xabc.htm (1261 words)

	unit02-sect02-les01-lessona (Site not responding. Last check: 2007-10-31)
		2 is a fourth root of 16 because 2
		In the case of the square root the index is 2.
		As with the square root, we have to be careful when dealing with the fourth root of variable expressions.
	www.cdli.ca /courses/math3103/unit02/section02/lesson01/3-lesson-a.htm (524 words)

	Algebra Help Software
		Since the principle square root is the positive square root, we have:
		When you square the square root of a nonnegative number, the result is the original number.
		Likewise, when you take the square root of a nonnegative number squared, the result is the original number.
	www.algebra-help.org /square-roots-4.html (226 words)

	Java 2 Platform SE v1.3.1: Class Math
		If the first argument is positive zero and the second argument is positive, or the first argument is positive and finite and the second argument is positive infinity, then the result is positive zero.
		If the first argument is positive zero and the second argument is greater than zero, or the first argument is positive infinity and the second argument is less than zero, then the result is positive zero.
		If the first argument is positive zero and the second argument is less than zero, or the first argument is positive infinity and the second argument is greater than zero, then the result is positive infinity.
	java.sun.com /j2se/1.3/docs/api/java/lang/Math.html (3130 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-31)
		Date: 10/24/2002 at 14:40:31 From: Arthur Subject: Principal Square Roots I was just wondering why it's always taught that the principal square root of a number is positive.
		Probably the main reason we choose the positive root is that positive numbers are more familiar and useful.
		In addition, if the principal root were negative, we could not say sqrt(a) * sqrt(b) = sqrt(ab) because, for example, sqrt(4) * sqrt(9) = -2 * -3 = 6 while sqrt(4*9) = sqrt(36) = -6 So it's a lot easier to take it the way we do.
	mathforum.org /library/drmath/view/61598.html (194 words)

	Roots, Coroots and Weights
		The number of positive roots of the root datum RD. This is also the number of positive coroots.
		The root alpha acts on the root space via the reflection s_alpha; the coroot alpha^star acts on the coroot space via the reflection s_alpha^star.
		The square of the length of the rth (co)root of the root datum RD.
	www.umich.edu /~gpcc/scs/magma/text482.htm (1015 words)

	Roots and Radical Expressions
		Since m could be any real number value, positive or negative, and the symbol used in the principal square root, we should indicate the absolute value of m to ensure the result is non-negative.
		–3 is the cube root of –27 because (–3)
		The cube root of a positive number is positive.
	www.jcoffman.com /Algebra2/ch7_1.htm (529 words)

	EMT 668 Assignment 3 (Site not responding. Last check: 2007-10-31)
		For any graph in the xb plane when a and c are positive we have the same possible roots, where part of the graph has two solutions, two points have one solution, and part has no solution.
		Therefore, we can say that for any graph in the xb plane, when a and c are positive, we have parts with two roots, two points with one root, and parts with no roots.
		We have also seen that in each plane, there are parts of the graph that have two roots, one root, or no roots.
	jwilson.coe.uga.edu /emt668/EMAT6680.2001/King/assign3/assign3.html (1498 words)

	Root Cause Analysis Training
		Root Cause Analysis (RCA) is a process designed to facilitate the investigation of the fundamental or root causes for undesired outcomes (e.g.
		Root Cause Analysis using the Creative Problem Solving process (RCA-CPS) is a powerful, flexible, and effective means of understanding any situation clearly, generating options and solutions, and converting those options into practice.
		Ensure that the root causes are identified for the problems of the greatest impact and highest priority.
	www.positive-way.com /business/root1.htm (618 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-31)
		Date: 11/24/98 at 17:56:58 From: Doctor Pat Subject: Re: Square Roots Andrew, The convention in mathematics is that x^2 = 81 has two solutions, x = 9 or x = -9, but when we take the square root of a value, we want the principal square root.
		It is important that you know that there are two values that may be squared to give every real number (even the negatives), but it is also important that you understand that we may want to make a distinction between all the particular roots of an equation, and the request to give a particular solution.
		Your teacher clearly wants you to give the positive square root of the value when the square root symbol is used.
	mathforum.org /library/drmath/view/58266.html (290 words)

	Chapter 9 Notes (Site not responding. Last check: 2007-10-31)
		The square roots of 25 are 5 and –5.
		The principal square root is the positive square root and is indicated by a √a.
		If "k" is even, "a" must be positive and there are two roots: one positive and one negative.
	mtsu32.mtsu.edu:11039 /chapter_9_notes.htm (163 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		The first is show that the whole numbers are equinumerous to the irrational numbers represented by the positive square roots.
		Proof: This is done by creating a matrix for each of the positive whole number roots in exactly the same manner as the one for square roots.
		Therefore, the natural numbers are equinumerous to the irrational numbers represented by positive whole number roots of rational numbers.
	www.public.iastate.edu /~joefish/proof.doc (382 words)

	Radicals and Roots (Site not responding. Last check: 2007-10-31)
		This business of roots has a bit of a twist in it depending on the index (n) of the radical sign.
		Note that in each case the positive root is the principle root.
		In the case of odd indices, there is only one root as indicated in the text (2).
	home.earthlink.net /~ubingc/math/mth209/roots.htm (813 words)

	A no hydrotropic response Root Mutant that Responds Positively to Gravitropism in Arabidopsis -- Eapen et al. 131 (2): ...
		The phenomenon of root responsiveness to moisture gradients is known as hydrotropism.
		Position "a" is where the two media are in contact; position "b" is where the root stopped growing or where root curvature took place in NM; position "c" is the middle position along the diagonal within NM; and position "d" is the upper limit of the WSM in the screening system.
		Kinetics of root gravitropic bending in wild-type and heterozygous nhr1 seedlings.
	www.plantphysiol.org /cgi/content/full/131/2/536 (7322 words)

	Square root - GameDev.Net Discussion Forums
		Therefore the square root of 16 is -4 and +4, and the square root of -16 is 4i.
		In fact the square root of -16 is 4i or -4i (the complex conjugate roots).
		The square roots of 4 are -sqrt(4), sqrt(4).
	www.gamedev.net /community/forums/topic.asp?topic_id=165527 (1505 words)

	SparkNotes: Polynomial Functions: Roots of Higher Degree Polynomials
		Finding the roots of higher degree polynomials is much more difficult than finding the roots of a quadratic function.
		and the denominator of the root is a factor of a
		Complex roots will not be discussed until after a thorough exploration of complex numbers and polar coordinates.
	www.sparknotes.com /math/precalc/polynomialfunctions/section5.rhtml (793 words)

	10.1: Radical Expressions (Site not responding. Last check: 2007-10-31)
		In other words, a principal square root is the positive root (except in the case of zero because the principal square root of zero is zero.).
		The square root symbol represents the principal root.
		One root is positive, and one root is negative.
	www.mtsu.edu /~mhiggs/101.html (463 words)

	Descartes’ Rule of Signs
		We know how many roots a polynomial has by the highest degree of the polynomial.
		The first term is positive, the second term is negative the third term is positive and the fourth term is negative.
		When we do look at the graph we see that there are 3 negative roots and 1 positive root.
	www.shs.d211.org /Math/MATHEMATICS/DescartesRuleofSigns.htm (459 words)

	Roots and Coroots
		The number of positive roots of the root system R. This is also the number of positive coroots.
		The index of the sum of the rth and sth roots in the crystallographic root system R, or 0 if the sum is not a root.
		Indices in the crystallographic root system R of the left string through alpha_s in the direction of alpha_r, i.e.
	www.math.wayne.edu /answers/magma2.10/htmlhelp/text977.htm (1162 words)

	PlanetMath: square root of positive definite matrix
		"square root of positive definite matrix" is owned by rspuzio.
		Cross-references: clear, properties, matrix, eigenvalues, unitary matrix, diagonalization, Hermitian matrix, positive definite
		This is version 8 of square root of positive definite matrix, born on 2005-05-17, modified 2006-09-05.
	planetmath.org /encyclopedia/SquareRootOfPositiveDefiniteMatrix.html (77 words)

	Roots (Site not responding. Last check: 2007-10-31)
		The common example is the square root, which “undoes” the act of squaring.
		The cube root, for example, is the inverse of raising to the power of 3.
		The cube root of 8 is 2 because 2
	www.jamesbrennan.org /algebra/radicals/square_roots.htm (489 words)

	Taking Square Roots
		I can understand that, because the square root sign denotes the positive square root, so in order to ensure the result is positive without making any assumptions about the intrinsic sign of k, you'd have to take its absolute value.
		To get the negative root, it is simply a matter of multiplying the positive root by -1, but only the positive root is THE square root.
		For the square root relation to be considered a function, it must be one-to-one (pass the vertical line test, loosely speaking).
	www.physicsforums.com /showthread.php?p=966242 (1137 words)

	PlanetMath:
		positive definite (=positive definite form) owned by djao
		positively homogeneous function (=homogeneous function) owned by matte
		probability that two positive integers are relatively prime owned by mps
	planetmath.org /encyclopedia/P (2842 words)

	Electrochemistry Encyclopedia --- Electrochemistry of plant life
		Electrical polarity in soybean, potato, tomato, and cacti coincides with the electrical field of the "electric double layer" of Earth: negative in roots and positive on the top of the plants.
		Figure 3 shows the positive spikes and negative humps that appear during measurement of electrical potential difference between two reversible silver/silver chloride electrodes.
		The reference electrode (negative) is generally inserted in the stem or in a root of a soybean.
	yces.case.edu /ed/encycl/art-p01-plants.htm (6636 words)

	Algebra Proof 2 (Site not responding. Last check: 2007-10-31)
		nth root of a is the nth root that has the same sign as a.
		The positive integer n is the index of the radical, and the number
		A common misunderstanding is that the square root sign both positive and negative square roots.
	www.qcc.mass.edu /hcook/algebra_proof_2.htm (191 words)

	Bisection Method Tutorial
		So long as the function whose root we are finding is continuous, there must be at least one root between the positive and negative guesses.
		The x-coordinate of this point is the average of the positive and negative guesses.
		There is also a "Zoom" menu in the menu bar.) At any point of the simulation, the average of the positive and negative guesses, which is displayed as the x-coordinate of the bisection point, will be an approximation to a root of f.
	www.cs.utah.edu /~zachary/isp/applets/Root/Bisection.html (718 words)

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