How to Understand the Ratio of Quadratic Roots?

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    Quadratic Ratio Roots
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Discussion Overview

The discussion revolves around understanding the ratio of roots of quadratic equations, particularly in the context of problem-solving for mathematical competitions like the Olympiad. Participants explore methods for deriving coefficients from these ratios.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • Some participants mention the importance of skills in solving problems related to quadratic ratios for Olympiad preparation.
  • One participant suggests that brute force methods may be necessary if speed is lacking during problem-solving.
  • Another participant describes a method of writing down the ratios and solving for one of the coefficients, indicating that any of the remaining coefficients could be solved similarly.
  • There is a request for clarification from a participant who expresses confusion about the problem, asking for more details on what specifically was not understood.

Areas of Agreement / Disagreement

Participants express differing levels of understanding regarding the problem, with some feeling confident in their approach while others are confused and seek clarification. No consensus is reached on the specific methods or solutions.

Contextual Notes

Some assumptions about the familiarity with quadratic equations and competition-level problem-solving may be present, but these are not explicitly stated. The discussion does not resolve the mathematical steps involved in finding the ratios or coefficients.

Mathsonfire
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Mathsonfire said:
86

Those are nice problems. If you're prepping for the Olympiad, you will need the skills. If all else fails, brute force it! Of course, if you're not fast enough, you'll waste too much time.

Personally, I wrote down the ratios and solved for b. You could solve for any of the 4 remaining arbitrary coefficients.

They were nice to you and made them both monic quadratics.
 
tkhunny said:
Those are nice problems. If you're prepping for the Olympiad, you will need the skills. If all else fails, brute force it! Of course, if you're not fast enough, you'll waste too much time.

Personally, I wrote down the ratios and solved for b. You could solve for any of the 4 remaining arbitrary coefficients.

They were nice to you and made them both monic quadratics.

I didnt get it
 
Mathsonfire said:
I didnt get it

Didn't get what? Ratios? Solve for...? Please provide YOUR work.
 

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