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

Embed

**Published on Mar 23, 2019**- How would the presence of triple roots affect the desired expression?

Your support is a heartfelt source of encouragement that propels the channel forward.

Please consider taking a second to subscribe in order to express your valuable support and receive notifications for the latest videos!

Any likes, subscriptions, comments, constructive criticisms, etc., are very much appreciated.

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

Shakeitpiggy26 days agoThianosaurus Rex

That makes sense! Thanks.

Thianosaurus Rex26 days 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)

Omar2 months agoshouldn't be better to note that

ΣΣkj for all k,j = Σ kj for j≥k + Σ kj for j

Brendan Chamberlain3 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.

LetsSolveMathProblems3 months ago^{+1}Of course! I'm glad you find them useful. =)

AKIB KHAN3 months ago^{+1}Very elegant approach.Thank You.

One in a billion3 months ago^{+3}For an A* CIE A level student like me, I can't even understand the question.

Sachin Sahay3 months agoMy favorite AIME question this year!

Nacho3 months agothe kids that do well in this are fucking geniouses

Chan Dan3 months ago^{+1}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.

LetsSolveMathProblems3 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:

artofproblemsolving.com/alcumus

2. George Pólya's "How to Solve It" is a classic book for developing a "problem-solving mindset."

Chan Dan3 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?

LetsSolveMathProblems3 months ago^{+2}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 Flores3 months ago^{+3}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 S3 months agoImpressive

Ganzrationaler Testudinadler3 months ago^{+3}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 FC3 months agoZed mate, not 'zee'.

Aryan Jain3 months ago^{+1}Depends on which english. Its "zee" in American english.

Adlet Irlanuly3 months ago^{+2}That is in essence beautiful.

LeoGD3 months ago^{+2}Beautiful

AV Drago3 months ago^{+1}The AIME 1 this year was much easier than the AIME 2.

引きこもり3 months agonice