Search results

  • ===Polynomial Inequalities=== The first part of solving polynomial inequalities is much like solving polynomial equations -- bringing all the terms to one side and finding the roots.
    12 KB (1,806 words) - 05:07, 19 June 2024
  • ...s Little Theorem]], every nonzero element of this field is a root of the [[polynomial]] == Problems ==
    4 KB (639 words) - 00:53, 2 February 2023
  • ...ession into factors, is to write the expression (often an [[integer]] or [[polynomial]]) as a product of different terms. This often allows one to find informat ...that could otherwise be solved by [[Newton sums]] or problems that give a polynomial and ask a question about the roots. Combined with [[Vieta's formulas]], th
    3 KB (532 words) - 21:00, 13 January 2024
  • ...ns of change, [[volume]]s of irregular [[solid]]s, and many other types of problems in mathematics. * [[Taylor polynomial]]
    2 KB (299 words) - 18:47, 30 June 2024
  • ...well as many [[math competitions]] is the use of creative methods to solve problems. In a way, students are discouraged to use rote memorization as opposed to ...<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>
    2 KB (314 words) - 05:45, 1 May 2014
  • ...e [[AM-GM Inequality]], Cauchy-Schwarz forms the foundation for inequality problems in intermediate and olympiad competitions. It is particularly crucial in pr ...ion comes in handy in linear algebra problems at intermediate and olympiad problems.
    13 KB (2,048 words) - 14:28, 22 February 2024
  • The discriminant can tell us something about the roots of a given [[polynomial]] <math>p(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_0</math> of degree <math>n</math> ...nt of a polynomial is the product of the squares of the differences of the polynomial roots <math>r_i</math>, so,
    4 KB (768 words) - 16:56, 24 June 2024
  • ...> where a, b, and c are [[constant]]s. This is useful for manipulating the polynomial. ==Problems==
    3 KB (551 words) - 15:22, 13 September 2023
  • ==Problems== ...h> are relatively prime integers, find <math> p+q. </math> ([[2005 AIME II Problems/Problem 15|Source]])
    5 KB (892 words) - 20:52, 1 May 2021
  • == Example Problems == ...u ask the oracle to do. Show that it is possible to uniquely determine the polynomial after only two consultations of the oracle. ([http://www.math.uiuc.edu/~hil
    4 KB (547 words) - 16:23, 30 December 2020
  • ...that could otherwise be solved by [[Newton sums]] or problems that give a polynomial, and ask a question about the roots. Combined with [[Vieta's formulas]], t
    2 KB (327 words) - 01:06, 28 April 2024
  • The number pi often shows up in problems in [[number theory]], particularly [[algebraic number theory]]. For example ...for every polynomial <math>R(x,y)</math> with integer coefficients whose [[polynomial|degree]] in both <math>x</math> and <math>y</math>
    8 KB (1,469 words) - 20:11, 16 September 2022
  • ...<math> x^2 = -1 </math> but we can now find ''all'' solutions to ''every'' polynomial. (See the [[Fundamental Theorem of Algebra]] for more details.) == Problems ==
    5 KB (860 words) - 14:36, 10 December 2023
  • == Problems == Here are some problems with solutions that utilize arithmetic sequences and series.
    4 KB (736 words) - 01:00, 7 March 2024
  • == Problems == ...n_2, </math> find the product <math> n_1\cdot n_2</math>. ([[2005 AIME II Problems/Problem 13|Source]])
    9 KB (1,434 words) - 00:15, 4 July 2024
  • ...th [[analytic geometry]], which is use of coordinates to solve geometrical problems. ...Euclidean" space.) Let <math>R=\mathbb{C}[X_1,\ldots,X_n]</math> be the [[polynomial ring]] in <math>n</math> variables, and let <math>I</math> be a [[prime ide
    2 KB (361 words) - 00:59, 24 January 2020
  • ...quations]], testing whether certain large numbers are prime, and even some problems in cryptology. ...ave a number of roots greater than its degree. Consider, for example, the polynomial congruence
    14 KB (2,317 words) - 18:01, 29 October 2021
  • [[2021 JMC 10 Problems/Problem 1|Solution]] [[2021 JMC 10 Problems/Problem 2|Solution]]
    12 KB (1,784 words) - 15:49, 1 April 2021
  • {{AMC12 Problems|year=2005|ab=A}} [[2005 AMC 12A Problems/Problem 1|Solution]]
    13 KB (1,965 words) - 21:18, 7 September 2024
  • {{AMC12 Problems|year=2004|ab=A}} [[2004 AMC 12A Problems/Problem 1|Solution]]
    13 KB (1,953 words) - 23:31, 25 January 2023

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