Vieta's with Triple Roots (2019 AIME I Problem 10)

  • Published on Mar 23, 2019
  • How would the presence of triple roots affect the desired expression?
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Comments • 24

  • Dean Yang
    Dean Yang Month ago

    Amazing solution

  • Shakeitpiggy
    Shakeitpiggy 3 months ago +1

    Why do they always ask for m+n instead of stopping at m/n? Is it just to keep you on your toes?

    • Shakeitpiggy
      Shakeitpiggy 3 months ago

      Thianosaurus Rex
      That makes sense! Thanks.

    • Thianosaurus Rex
      Thianosaurus Rex 3 months ago +1

      Because every answer has to be given as an integer between 0 and 999 (so computers can check the answers more easily i guess)

  • Omar
    Omar 5 months ago

    shouldn't be better to note that
    ΣΣkj for all k,j = Σ kj for j≥k + Σ kj for j

  • Brendan Chamberlain
    Brendan Chamberlain 5 months ago +1

    Thank you so much for making these videos! I like watching these in addition to reading the AOPS books in my free time haha. Very clear explanation as always.

    AKIB KHAN 5 months ago +1

    Very elegant approach.Thank You.

  • One in a billion
    One in a billion 5 months ago +5

    For an A* CIE A level student like me, I can't even understand the question.

  • Sachin Sahay
    Sachin Sahay 5 months ago

    My favorite AIME question this year!

  • Nacho
    Nacho 5 months ago

    the kids that do well in this are fucking geniouses

  • Chan Dan
    Chan Dan 5 months ago +2

    I always try to give a shot to these kind if problems but i dont know where to start, please anyone give me a reference book to start.

    • LetsSolveMathProblems
      LetsSolveMathProblems  5 months ago +2

      @Chan Dan Yes, I was referring to the book by Rusczyk and Lehoczky. I am surprised that it is approximately twice as expensive in India. If you cannot buy a used copy at a more affordable price, I again wholeheartedly recommend Paul Zeitz's "Art and Craft of Problem Solving" for a great exposition on problem solving. Here are a few additional recommendations I did not mention in the previous comment:
      1. Art of Problem Solving Website's Alcumnus is, from what I can tell, an outstanding (and free!) tool for learning new ideas and solidifying your mathematical foundation:
      2. George Pólya's "How to Solve It" is a classic book for developing a "problem-solving mindset."

    • Chan Dan
      Chan Dan 5 months ago +1

      @LetsSolveMathProblemsthanks sir ! are you talking about the book by sandor lehozky and Richard rusczyk ?actually it is nearly $100 in india for the volume 2,any alternative for volume 2?

    • LetsSolveMathProblems
      LetsSolveMathProblems  5 months ago +3

      If you are a beginner to high school level mathematical problem solving, I would first recommend "Art of Problem Solving Volumes 1 and 2" without hesitation. The main concept you probably should be acquainted with to solve this particular problem, called Vieta's formulas, is discussed in Volume 2. Aside from the outstanding Art of Problem Solving series, other excellent problem solving books include Paul Zeitz's "Art and Craft of Problem Solving" and, once you have a good degree of mathematical maturity, Arthur Engel's "Problem Solving Strategies."

  • Daniel Flores
    Daniel Flores 5 months ago +4

    When I tried this problem It sounded impossible to solve given the available info, but then after a couple of minutes I SOLVED IT :D 352 haha i cant believe it was solvable

    • N S
      N S 5 months ago +1


  • Ganzrationaler Testudinadler

    In what way is it relevant if the z_i are complex? Does it have an effect on the possibilities to express the polynomial?

  • Portsmouth FC
    Portsmouth FC 5 months ago

    Zed mate, not 'zee'.

    • AJ9101
      AJ9101 5 months ago +1

      Depends on which english. Its "zee" in American english.

  • Adlet Irlanuly
    Adlet Irlanuly 5 months ago +2

    That is in essence beautiful.

  • LeoGD
    LeoGD 5 months ago +2


  • AV Drago
    AV Drago 5 months ago +1

    The AIME 1 this year was much easier than the AIME 2.

  • 引きこもり
    引きこもり 5 months ago