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• Collatz Problem
  ...path will be followed by <math>n</math> as it was for <math>b</math>; any time the lead coefficient still has a factor of 2.
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• Modular arithmetic/Intermediate
  ...ave a number of roots greater than its degree. Consider, for example, the polynomial congruence This time, factoring the expression on the left yields
  14 KB (2,317 words) - 19:01, 29 October 2021
• 2021 JMC 10
  ...eling from a cell to another cell, it takes one of the paths with shortest time. The particle starts at cell <math>A</math> and travels to cell <math>B</ma ...\le 4.</math> What is the coefficient of the <math>x^4</math> term in the polynomial <math>Q(x)?</math>
  12 KB (1,784 words) - 16:49, 1 April 2021
• 2005 AMC 12A Problems
  ...oward Josh's house. When they met, Josh had ridden for twice the length of time as Mike and at four-fifths of Mike's rate. How many miles had Mike ridden w ...- 3)</math>. For how many polynomials <math>Q(x)</math> does there exist a polynomial <math>R(x)</math> of degree 3 such that <math>P(Q(x)) = P(x) \cdot R(x)</ma
  13 KB (1,971 words) - 13:03, 19 February 2020
• 2002 AMC 12A Problems
  ...many miles per hour does Mr. Bird need to drive to get to work exactly on time? ...h>P</math> with real coefficients are all replaced by their mean to form a polynomial <math>Q</math>. Which of the following could be a graph of <math>y = P(x)</
  12 KB (1,792 words) - 13:06, 19 February 2020
• 2001 AMC 12 Problems
  ...y five chips, three red and two white. Chips are randomly removed one at a time without replacement until all the red chips are drawn or all the white chip The polynomial <math>P(x)=x^3+ax^2+bx+c</math> has the property that the mean of its zeros
  13 KB (1,957 words) - 12:53, 24 January 2024
• 1984 AIME Problems/Problem 15
  ...</math>, we can express the difference of the two polynomials by a quartic polynomial that has roots at <math>t=4,16,36,64</math>, so ...ver following this unless you have no idea what to do with an hour of your time. Even so, learning the above solutions will be more beneficial.
  6 KB (1,051 words) - 04:52, 8 May 2024
• 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 (1,585 words) - 03:58, 1 May 2023
• 1996 AIME Problems/Problem 5
  By [[Vieta's formulas]] on the polynomial <math>P(x) = x^3+3x^2+4x-11 = (x-a)(x-b)(x-c) = 0</math>, we have <math>a + As we know that the sum of the roots of the first polynomial, <math>a+b+c</math> is <math>-3</math> by applying Vieta's again.
  3 KB (585 words) - 22:08, 19 November 2022
• 2003 AIME II Problems/Problem 13
  As a note, do NOT do this on the exam as it will eat up your time, but feel free to experiment around with this if you have a good enough und ...lambda}{4} + \frac{1}{4}</math>, and extracting eigenvalues by setting the polynomial equal to <math>0</math>, we have 2 eigenvalues: <math>\lambda_1 = 1</math>
  15 KB (2,406 words) - 23:56, 23 November 2023
• P versus NP
  ...lems that can be solved by a ''non-deterministic'' algorithm in polynomial time. The <math>P</math> versus <math>NP</math> question asks whether these two ...solve a problem). In such analysis, a [[model]] of the computer for which time must be analyzed is required. Typically, such models assume that the comput
  6 KB (1,104 words) - 15:11, 25 October 2017
• 2007 iTest Problems
  ...half mile from the point where it will enter the tunnel. At that point in time, Joe can run toward the train and just exit the tunnel as the train meets h NO SOLUTION HERE! PLEASE TRY AGAIN NEXT TIME
  30 KB (4,794 words) - 23:00, 8 May 2024
• Mock AIME 2 Pre 2005/Problems
  ...and a black ball. These balls are randomly drawn out of the box one at a time (without replacement) until two of the same color have been removed. This <math>P(x)</math> is the polynomial of minimal degree that satisfies
  6 KB (990 words) - 15:23, 11 November 2009
• 2007 AIME I Problems
  ...of these three persons is exactly halfway between the other two. At that time, find the distance in feet between the start of the walkway and the middle The polynomial <math>P(x)</math> is cubic. What is the largest value of <math>k</math> fo
  7 KB (1,218 words) - 15:28, 11 July 2022
• 2007 AIME II Problems
  ...rs in a factory produce widgets and whoosits. For each product, production time is [[constant]] and identical for all workers, but not necessarily equal fo Let <math>f(x)</math> be a [[polynomial]] with real [[coefficient]]s such that <math>f(0) = 1,</math> <math>f(2)+f(
  9 KB (1,435 words) - 01:45, 6 December 2021
• 2007 AMC 12A Problems
  ...s 7 times as fast as he walks, and both choices require the same amount of time. What is the [[ratio]] of Yan's distance from his home to his distance from The [[polynomial]] <math>f(x) = x^{4} + ax^{3} + bx^{2} + cx + d</math> has real [[coefficie
  11 KB (1,750 words) - 13:35, 15 April 2022
• LaTeX:Commands
  Notice that we can apply both a subscript and a superscript at the same time. For subscripts or superscripts with more than one character, you must surr The characteristic polynomial $f(\lambda)$ of the
  12 KB (1,898 words) - 15:31, 22 February 2024
• 1999 AHSME Problems
  ...ber of points of intersection of the graphs of two different fourth degree polynomial functions <math>y = p(x)</math> and <math>y = q(x)</math>, each with leadin ...nd Hana - sang songs in a concert as trios, with one girl sitting out each time. Hanna sang 7 songs, which was more than any other girl, and Mary sang 4 so
  13 KB (1,945 words) - 18:28, 19 June 2023
• 1959 AHSME Problems
  What is <math>B</math>'s time to run around the track, expressed in seconds? Given the polynomial <math>a_0x^n+a_1x^{n-1}+\cdots+a_{n-1}x+a_n</math>, where <math>n</math> is
  22 KB (3,345 words) - 20:12, 15 February 2023
• 2008 Mock ARML 2 Problems
  ...of a function, <math>f(x)</math>. He reveals to Bob that the function is a polynomial of the form <math>f(x) = ax^8 + bx^5 + cx^2 + dx + e</math>, where <math>a< ...t row, which contains <math>32</math> blocks. John removes blocks one at a time, removing only blocks that currently have no blocks on top of them. Find th
  4 KB (582 words) - 21:57, 8 May 2019
• Approximation Techniques
  ...lems which are considered "intractable", i.e. no known "quick" (polynomial-time) [[algorithm]] is known for their solution. Heuristic algorithms quickly co ...egime. For instance, a long-time solution may be valid over "intermediate" time-scales as well. (Eg, for any t greater than 1.)
  2 KB (322 words) - 21:03, 11 February 2009
• KGS math club
  ...1 ranks (0 to 10). A parade is a sequence of cards played one by one; each time a card is played at the end of the sequence, count that number back, and fr |Prove or disprove: If P(x) is a polynomial (with non-zero degree) of one real variable and a and b satisfy <math>P^{(n
  22 KB (3,358 words) - 15:17, 18 July 2017
• Millennium Problems
  ...cts on their field of mathematics and beyond, and were all unsolved at the time of the offering of the prize. ...nyone who could solve one of the seven most difficult open problems at the time.
  13 KB (1,969 words) - 17:57, 22 February 2024
• 2008 iTest Problems
  ...ch he takes <math>40</math> nickels out of a roll and tosses them one at a time toward his desk where his change jar sits. He awards himself <math>5</math> ...long time friend of the family. An unusual fellow, Dr. Lisi spends as much time surfing
  71 KB (11,749 words) - 01:31, 2 November 2023
• Polynomial ring
  Given a [[ring]] <math>R</math>, the '''polynomial ring''' <math>R[x]</math> is, informally, "the ring of all polynomials in a ...ements of <math>R[x]</math> '''polynomials''' (over <math>R</math>). For a polynomial <math>p=(a_0,a_1,a_2,\ldots)</math>, the terms <math>a_0,a_1,a_2,\ldots</ma
  12 KB (2,010 words) - 00:10, 3 August 2020
• Hilbert's Basis Theorem
  series, either, but I don't have time to prove it this evening.--> is theology.]" In time, though, the value of nonconstructive
  4 KB (617 words) - 19:59, 23 April 2023
• 2010 AMC 10A Problems
  ...h> hours including the stop. Which equation could be used to solve for the time <math>t</math> in hours that she drove before her stop? The polynomial <math>x^3 -ax^2 + bx -2010</math> has three positive integer roots. What is
  13 KB (1,902 words) - 11:20, 5 March 2023
• 2010 AIME I Problems/Problem 15
  ...m]] to reveal that <math>6x</math> is an integer because we can divide the polynomial by <math>2</math>. The only such <math>x</math> in the above-stated range i ...t I actually believe appears in Mandelbrot 1995-2003, or some book in that time-range).
  14 KB (2,210 words) - 13:14, 11 January 2024
• 2010 AIME II Problems/Problem 7
  ...h will give us <math>a+b+c+1</math>. Plugging in <math>z=1</math> into our polynomial, we get <math>(-3)(-3-6i)(-3+6i)</math> which evaluates to <math>-135</math
  4 KB (735 words) - 02:41, 27 June 2022
• 2011 AMC 10A Problems/Problem 22
  ...ath> ways, except we must subtract the number of ways for a triangle. Each time, there is <math>1</math> less vertex, so <math>5</math> times less ways to ...two adjacent vertices share the same color. In other words, it gives us a polynomial in terms of <math>k</math> where we can plug in <math>k=6</math> to get our
  14 KB (2,425 words) - 09:13, 5 November 2023
• Alcumus
  ...away XP. The quests are missions that must be done in a limited amount of time to earn. There is a log at the bottom left. It shows recent problems you've If the answer is a polynomial, put your answer in decreasing degree order. For example, use x^2+3x+2 inst
  3 KB (533 words) - 10:55, 7 February 2023
• 2012 AMC 12A Problems
  ...<math>\text{8:00 AM}</math>, and all three always take the same amount of time to eat lunch. On Monday the three of them painted <math>50\%</math> of a h Consider the polynomial
  14 KB (2,197 words) - 13:34, 12 August 2020
• 2014 USAMO Problems
  ...ath> and all zeros <math>x_1, x_2, x_3,</math> and <math>x_4</math> of the polynomial <math>P(x)=x^4+ax^3+bx^2+cx+d</math> are real. Find the smallest value the ...math>B</math> may choose any counter on the board and remove it. If at any time there are <math>k</math> consecutive grid cells in a line all of which cont
  3 KB (496 words) - 02:14, 14 February 2024
• 2012 AIME I Problems
  ...ath>4,</math> and <math>2.5</math> miles per hour, respectively. The first time Butch and Sundance meet at a milepost, they are <math>n</math> miles from D ...numbers <math>a,</math> <math>b,</math> and <math>c</math> are zeros of a polynomial <math>P(z) = z^3 + qz + r,</math> and <math>|a|^2 + |b|^2 + |c|^2 = 250.</m
  10 KB (1,617 words) - 14:49, 2 June 2023
• Mock AIME I 2012 Problems
  Consider the polynomial <math>p(x)=3x^2+2x+1</math>. Let <math>p^n (x) = p(p^{n-1}(x))</math> and < Let <math>P(x)</math> be a polynomial of degree 10 satisfying <math>P(x^2) = P(x)P(x-1)</math>. Find the maximum
  7 KB (1,309 words) - 11:13, 8 April 2012
• 1988 USAMO Problems/Problem 5
  Let <math>p(x)</math> be the polynomial <math>(1-x)^a(1-x^2)^b(1-x^3)^c\cdots(1-x^{32})^k</math>, where <math>a, b, ...everse the order of the coefficients of each factor, then we will obtain a polynomial whose coefficients are exactly the coefficients of <math>p(x)</math> in rev
  8 KB (1,348 words) - 09:44, 25 June 2022
• 1980 AHSME Problems
  The degree of <math>(x^2+1)^4 (x^3+1)^3</math> as a polynomial in <math>x</math> is ...th>\left(1, \frac 12 \right)</math>. If it continues in this fashion, each time making a <math>90^\circ</math> degree turn counterclockwise and traveling h
  15 KB (2,302 words) - 10:47, 30 April 2021
• ASIA TEAM Problems
  ...er <math>r</math> such that Kelvin will reach <math>1</math> for the first time in <math>r</math> jumps. In particular, <math>o(1)=0</math> because Kelvin 0) Let the amount of flies on <math>a_i</math> at a given time be <math>S_i</math>.
  10 KB (1,710 words) - 23:23, 10 January 2020
• 1969 AHSME Problems
  ...onstant. If the second mile is traversed in <math>2</math> hours, then the time, in hours, needed to traverse the <math>n</math>th mile is: ...}-u_n=3+4(n-1), n=1,2,3\cdots.</math>If <math>u_n</math> is expressed as a polynomial in <math>n</math>, the algebraic sum of its coefficients is:
  16 KB (2,662 words) - 14:12, 20 February 2020
• 1987 AHSME Problems
  ...ing the letter on top of the pile in the secretary's in-box. When there is time, the secretary takes the top letter off the pile and types it. If there are How many polynomial functions <math>f</math> of degree <math>\ge 1</math> satisfy
  16 KB (2,291 words) - 13:45, 19 February 2020
• 1983 AHSME Problems
  ...math>1+\frac{2}{x} + \frac{3}{x^2}</math> are multiplied, the product is a polynomial of degree Let <math>f</math> be a polynomial function such that, for all real <math>x</math>,
  15 KB (2,309 words) - 23:43, 2 December 2021
• 2016 AMC 12A Problems
  ...negative direction. The probability that he reaches <math>4</math> at some time during this process is <math>\frac{a}{b},</math> where <math>a</math> and < ...xists a positive real number <math>b</math> such that all the roots of the polynomial <math>x^3-ax^2+bx-a</math> are real. In fact, for this value of <math>a</ma
  15 KB (2,348 words) - 17:20, 19 January 2024
• 2014 UNM-PNM Statewide High School Mathematics Contest II Problems
  ...ho is at least a year older than her siblings took the AMC 8 for the first time this year.” integers is a polynomial of degree <math>k + 1</math>, i.e.,
  5 KB (774 words) - 06:07, 29 January 2019
• 2015 UNCO Math Contest II Problems
  The positive integers are <math>1, 2, 3, 4, \ldots </math> A polynomial is quadratic if its highest power term has power two. If P is a polynomial that satisfies <math>P(x^2 +1) = 5x^4 +7x^2 +19</math>, then what is <math>
  7 KB (1,151 words) - 15:11, 20 August 2020
• 2015 AMC 10A Problems/Problem 16
  It may save some time to find two solutions, <math>(0, 0)</math> and <math>(5, 5)</math>, at this ...you divide both sides by <math>x(x-5)</math>. This can also be done using polynomial division to find <math>x = 5</math> as a factor. This gives
  7 KB (1,197 words) - 11:49, 5 February 2024
• 2015 AIME II Problems/Problem 14
  As with the other solutions, factor. But this time, let <math>a=xy</math> and <math>b=x+y</math>. Then <math>a^4b=810</math>. ...math> into <math>x^3 \cdot y^6 + y^3 \cdot x^6 = 945</math>. However, this time we only factor as <math>(xy)^3 \cdot (x^3 + y^3)</math> because we particul
  10 KB (1,751 words) - 22:21, 26 November 2023
• Algebraic number theory
  ...math>th root of unity. However, though this was not well-understood at the time, the implicit assumption was that <math>\mathbb{Z}[\omega]</math> was a [[p ...be shown that a number is an algebraic integer if and only if its minimal polynomial has integer coefficients.
  10 KB (1,646 words) - 15:04, 28 May 2020
• 2016 AMC 12A Problems/Problem 24
  ...xists a positive real number <math>b</math> such that all the roots of the polynomial <math>x^3-ax^2+bx-a</math> are real. In fact, for this value of <math>a</ma Let the roots of the polynomial be <math>r, s, t</math>. By Vieta's formulas we have <math>r+s+t=a</math>,
  3 KB (568 words) - 17:14, 20 April 2024
• 2017 UNM-PNM Statewide High School Mathematics Contest II Problems
  Find a second-degree polynomial with integer coefficients, <math>p(x) = ax^2 + bx + c</math>, such that <ma ...n the remaining stack each weigh <math>9.9</math> grams. You are given one time access to a precise digital scale. Devise a plan to weigh some coins in pre
  5 KB (846 words) - 03:36, 19 January 2019
• 2016 AMC 12B Problems/Problem 25
  ...n=b_{n-1}+2b_{n-2}</math> for all <math>n\geq 2</math>. The characteristic polynomial of this linear recurrence is <math>x^2-x-2=0</math>, which has roots <math> ...b_n = b_{n-1}+2b_{n-2}</math> (modulo <math>19</math> to save calculation time), we get the sequence
  4 KB (735 words) - 19:10, 11 January 2024
• 2017 AMC 10A Problems/Problem 24
  ...e distinct roots, and each root of <math>g(x)</math> is also a root of the polynomial <cmath>f(x) = x^4 + x^3 + bx^2 + 100x + c.</cmath>What is <math>f(1)</math> ..., three of which are roots of <math>g(x)</math>. Using the fact that every polynomial has a unique factorization into its roots, and since the leading coefficien
  10 KB (1,708 words) - 23:16, 7 October 2023
• 2017 AMC 12A Problems/Problem 23
  ...e distinct roots, and each root of <math>g(x)</math> is also a root of the polynomial <cmath>f(x) = x^4 + x^3 + bx^2 + 100x + c.</cmath>What is <math>f(1)</math> ..., three of which are roots of <math>g(x)</math>. Using the fact that every polynomial has a unique factorization into its roots, and since the leading coefficien
  10 KB (1,861 words) - 10:47, 17 October 2021
• 2017 AMC 10A Problems
  ...Mia and her mom to put all <math>30</math> toys into the box for the first time? ...e starting point is <math>S=2520</math>. Let <math>T>0</math> be the least time, in minutes, such that at least 5 of the horses are again at the starting p
  15 KB (2,285 words) - 18:02, 28 October 2023
• 2017 AMC 12A Problems
  ...tarting point is <math>S = 2520</math>. Let <math>T>0</math> be the least time, in minutes, such that at least <math>5</math> of the horses are again at t ...ad snowstorm and reduces her speed by <math>20</math> miles per hour. This time the trip takes her a total of <math>276</math> minutes. How many miles is t
  15 KB (2,418 words) - 16:58, 7 November 2022
• 2018 AIME II Problems
  ...ard <math>A</math>. Paul and Ina both arrive at <math>B</math> at the same time. Find the number of meters from <math>A</math> to <math>B</math>. ...the interval <math>[-20, 18]</math>. The probability that the roots of the polynomial
  9 KB (1,385 words) - 00:26, 21 January 2024
• 2018 AIME I Problems/Problem 12
  ...the same number. But can we extend this reasoning to all subcases to save time? ...{2\pi i/3}</math> is a cube root of unity, then it is well know that for a polynomial <math>P(x)</math>,
  26 KB (4,044 words) - 13:58, 24 January 2024
• 2019 AIME I Problems
  ...he game may be replaced later. No two substitutions can happen at the same time. The players involved and the order of the substitutions matter. Let <math> ...4)</math> and moves until it hits one of the coordinate axes for the first time. When the particle is at the point <math>(a,b)</math>, it moves at random t
  8 KB (1,331 words) - 06:57, 4 January 2021
• 2019 AMC 12B Problems
  ...th <math> \$1</math>. A bell rings every <math>15</math> seconds, at which time each of the players who currently have money simultaneously chooses one of ...he set of roots equals the set of coefficients? (For clarification: If the polynomial is <math>ax^2+bx+c,a\neq 0,</math> and the roots are <math>r</math> and <ma
  16 KB (2,477 words) - 15:41, 9 September 2023
• 2019 AIME I Problems/Problem 10
  For distinct complex numbers <math>z_1,z_2,\dots,z_{673}</math>, the polynomial ...{2019} + 20x^{2018} + 19x^{2017}+g(x)</math>, where <math>g(x)</math> is a polynomial with complex coefficients and with degree at most <math>2016</math>. The su
  10 KB (1,689 words) - 17:02, 8 February 2024
• Mock AIME 2 Pre 2005 Problems
  ..., and a black ball. These balls are randomly drawn out of the box one at a time (without replacement) until two of the same color have been removed. This p <math>P(x)</math> is a polynomial of minimal degree that satisfies <cmath>P(k) = \dfrac{1}{k(k+1)}</cmath> fo
  6 KB (1,052 words) - 13:52, 9 June 2020
• 2021 AMC 10A Problems
  ...cond and accelerating so that during each successive <math>1</math>-second time interval, it travels <math>7</math> inches more than during the previous <m All the roots of the polynomial <math>z^6-10z^5+Az^4+Bz^3+Cz^2+Dz+16</math> are positive integers, possibly
  15 KB (2,302 words) - 23:41, 14 April 2024
• 2021 HMC 10
  ...on after the <math>2</math>nd time he walked backward and <math>4th</math> time he walked forward. Let <math>f(x)</math> be a polynomial with degree of <math>5</math> such that <math>f(-2)=f(-1)=f(1)=f(2)=f(3)=13
  11 KB (1,745 words) - 16:44, 6 October 2021
• AMC 12C 2020 Problems
  ...ath>4</math> red marbles. If each marble is pulled out <math>1</math> at a time, what is the probability that the <math>6th</math> marble pulled out red? Let <math>P(x)</math> be a cubic polynomial with integral coefficients and roots <math>\cos \frac{\pi}{13}</math>, <mat
  8 KB (1,223 words) - 15:02, 27 November 2022
• 2022 AMC 12B Problems
  For how many values of the constant <math>k</math> will the polynomial <math>x^{2}+kx+36</math> have two distinct integer roots? ...two properties. What is the sum of the squares of the coefficients of that polynomial?
  15 KB (2,233 words) - 13:02, 10 November 2023
• 2020 CAMO Problems
  ...(x)=x^2-2</math>. Prove that for all positive integers <math>n</math>, the polynomial <cmath>P(x)=\underbrace{f(f(\ldots f}_{n\text{ times}}(x)\ldots))-x</cmath> ...tomatically wins. Moreover, the squid is claustrophobic, so at no point in time is it ever surrounded by a closed loop of black or gray squares. On Eric's
  4 KB (734 words) - 14:09, 5 September 2020
• 2021 AIME II Problems/Problem 7
  ...ath>. Thus we get polynomial <math>b^2+3b-10</math>. The discriminant this time is <math>49</math>, so we get two values for <math>b</math>. Through simple
  10 KB (1,680 words) - 00:20, 28 April 2024
• 2022 AMC 10B Problems
  the donkey hiccups regularly every <math>5</math> seconds. At what time does the donkey’s <math>700</math>th hiccup occur? For how many values of the constant <math>k</math> will the polynomial <math>x^{2}+kx+36</math> have two distinct integer roots?
  15 KB (2,224 words) - 13:10, 20 February 2024
• 2022 AMC 10A Problems/Problem 16
  The roots of the polynomial <math>10x^3 - 39x^2 + 29x - 6</math> are the height, length, and width of a Let <math>a</math>, <math>b</math>, <math>c</math> be the three roots of the polynomial. The lengthened prism's volume is <cmath>V = (a+2)(b+2)(c+2) = abc+2ac+2ab+
  7 KB (1,111 words) - 21:00, 21 February 2024
• 2022 AMC 12B Problems/Problem 11
  Every time <math>n</math> is multiple of <math>3</math> as is true when <math>n=2022</ == Solution 5 (Polynomial + Recursion) ==
  5 KB (866 words) - 22:17, 27 October 2023
• YWANG Generalization
  ...ring of more than one element of the form <math>(x-a_i)</math> at the same time. ...h>x=\infty</math>. A rigorous proof with both methods will be added in due time.
  2 KB (451 words) - 17:24, 23 February 2023
• 2023 AIME II Problems/Problem 8
  ...the exponents. We can now rewrite the exponents of each product (two at a time, where <math>1</math> is treated as the identity) as a series of arrays: where <math>r,s,t</math> are the roots of the polynomial <math>x^3+x+1=0</math>.
  9 KB (1,284 words) - 23:37, 31 January 2024
• 2023 AMC 10A Problems
  ...ards <math>B</math> at <math>18</math> miles per hour. Leaving at the same time, Beth bikes toward <math>A</math> at <math>12</math> miles per hour. How ma ...ting with a radius of <math>1</math> and increasing by <math>1</math> each time, all sharing a common point. The region between every other circle is shade
  16 KB (2,411 words) - 00:18, 7 May 2024
• 2022 SSMO Accuracy Round Problems
  A monic polynomial <math>f</math> has real roots <math>r,s,t.</math> A monic polynomial <math>g</math> has roots <math>r^3,s^3,t^3.</math> Given that the minimum p ...<math>60</math> miles per hour, the robber switches into a new car with no time loss. A police car can drive at a constant speed of 117 miles per hour. Giv
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