Create the page "Constant polynomial" on this wiki! See also the search results found.

• Polynomial
  ...lgebra]] often an arbitrary [[field]]). Note that a [[constant]] is also a polynomial. ...a polynomial will be equal to 1. In this case, we say we have a ''monic'' polynomial.
  6 KB (1,100 words) - 15:57, 30 August 2024
• Mathematical problem solving
  ...<math>\pm{2\pi}</math>, etc. so Euler made the leap of claiming that the [[polynomial]] on the right hand side can be factored as<br> The constant terms of both sides agree, both being 1, so this crazy procedure might be v
  2 KB (314 words) - 06:45, 1 May 2014
• Cauchy-Schwarz Inequality
  ...+ \cdots + a_nb_n)^2,</cmath> with equality if and only if there exists a constant <math>t</math> such that <math>a_i = t b_i</math> for all <math>1 \leq i \l Consider the polynomial of <math> t </math>
  13 KB (2,048 words) - 15:28, 22 February 2024
• Parabola
  ...> where a, b, and c are [[constant]]s. This is useful for manipulating the polynomial. ...<math>y^2</math><math>=4px</math> or <math>x^2=4py</math> where the p is a constant, and is the distance from the focus to the vertex.
  3 KB (551 words) - 16:22, 13 September 2023
• Ellipse
  ...sum of the distances from <math>P</math> to two fixed [[focus|foci]] is a constant. (The equivalence of these two definitions is a non-trivial fact.) * [[Polynomial]]s
  5 KB (892 words) - 21:52, 1 May 2021
• Pi
  ...84626433832795028841971693993751</math>. Pi is one of the most important [[constant]]s in all of mathematics and appears in many surprising places. The number ...beautiful results in mathematics since it involves five of the greatest [[constant]]s: [[e]], <math>\pi</math>, [[i]], [[1]], and [[0]].
  8 KB (1,424 words) - 16:49, 17 February 2025
• Arithmetic sequence
  ...ch that the difference between any two consecutive terms is constant. This constant is called the '''common difference''' of the sequence. * Find the roots of the polynomial <math>x^5-5x^4-35x^3+ax^2+bx+c</math>, given that the roots form an arithme
  4 KB (736 words) - 02:00, 7 March 2024
• Transcendental number
  ...[[polynomial]] with [[integer|integral]] [[coefficient]]s. Many famous [[constant]]s such as [[pi | <math>\pi</math>]] and [[e | <math>e</math>]] are transce
  568 bytes (72 words) - 11:52, 9 December 2007
• Fundamental Theorem of Algebra
  The '''fundamental theorem of algebra''' states that every [[nonconstant]] [[polynomial]] with [[complex number|complex]] [[coefficient]]s has a complex [[root]]. ...th>n</math> complex roots, counting multiplicities. In other words, every polynomial over <math>\mathbb{C}</math> splits over <math>\mathbb{C}</math>, or decomp
  5 KB (832 words) - 14:22, 11 January 2024
• Rational approximation of famous numbers
  ==Magic Polynomial== ...useful polynomial that often appears in proofs of irrationality. It is the polynomial
  8 KB (1,431 words) - 13:48, 26 January 2008
• 2022 AIME I Problems/Problem 1
  ...d <math>Q(x)</math> cancel, we conclude that <math>R(x)</math> is a linear polynomial. ...equation of <math>R(x)</math> is <cmath>R(x)=-\frac12x+c</cmath> for some constant <math>c,</math> and we wish to find <math>R(0)=c.</math>
  4 KB (670 words) - 13:03, 13 November 2023
• 2021 JMC 10
  ...\le 4.</math> What is the coefficient of the <math>x^4</math> term in the polynomial <math>Q(x)?</math> An invisible ant and an anteater, at the same constant speed of <math>1</math> edge length per second, start at (not necessarily d
  12 KB (1,784 words) - 16:49, 1 April 2021
• 2004 AMC 12A Problems
  ...math>150</math> meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters? A [[polynomial]]
  13 KB (1,953 words) - 00:31, 26 January 2023
• 2000 AMC 12 Problems
  are arranged in increasing order, they form a non-constant [[arithmetic progression]]. What is the sum of all possible real values of ...[[graph]] below shows a portion of the [[curve]] defined by the quartic [[polynomial]] <math>P(x) = x^4 + ax^3 + bx^2 + cx + d</math>. Which of the following is
  13 KB (1,948 words) - 10:35, 16 June 2024
• Root (polynomial)
  A '''root''' of a [[function]] (often a [[polynomial]]) <math>f(x)</math> whose range is the [[real number | real]], the [[compl ...thbb C</math> and <math>c_n \neq 0</math>, a general degree-<math>n</math> polynomial. The degree of <math>P(x)</math> is <math>n</math>, so <math>P(x)</math> ha
  8 KB (1,427 words) - 21:37, 13 March 2022
• Constant
  A '''constant''' is a number with fixed value, unlike a [[variable]] that can change or t The word constant is also used in other contexts or as part of other expressions:
  1 KB (241 words) - 19:39, 30 January 2007
• 2004 AIME I Problems/Problem 7
  Let our [[polynomial]] be <math>P(x)</math>. ...o <math>P(x) = 1 -8x + Cx^2 + Q(x)</math>, where <math>Q(x)</math> is some polynomial [[divisibility | divisible]] by <math>x^3</math>.
  7 KB (1,099 words) - 13:41, 30 December 2024
• 1983 AIME Problems/Problem 3
  ...were to expand by squaring, we would get a [[quartic Equation|quartic]] [[polynomial]], which isn't always the easiest thing to deal with. ...noticing that the polynomial on the left is <math>15</math> less than the polynomial under the radical sign. Thus: <cmath>(x^2+ 18x + 45) - 2\sqrt{x^2+18x+45} -
  3 KB (532 words) - 13:05, 29 November 2024
• 1986 AIME Problems/Problem 11
  ...7}y^{17}</math>, where <math>y=x+1</math> and the <math>a_i</math>'s are [[constant]]s. Find the value of <math>a_2</math>. Let <math>\vec{v} \in V</math> be the polynomial given in the problem, and it is easy to see that <math>[ \vec{v} ]_B = \lan
  6 KB (872 words) - 16:51, 9 June 2023
• 1988 AIME Problems/Problem 13
  ...on|recursive definition, <math>F_{n+2} - F_{n+1} - F_n = 0</math>, and the polynomial <math>x^2 - x - 1 = 0</math>. ...attern, such as repeated substitution of <math>x^2 = x + 1</math> into the polynomial with a higher degree, as shown in Solution 6.
  10 KB (1,595 words) - 16:30, 24 August 2024

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)