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Packet 3: Bonus 17

The first explicit solution to this equation was created by Brahmagupta, though two signs are different from the modern version. For 10 points each:
[10e] Name this mathematical equation, whose roots are given by [read slowly] negative b plus or minus the square root of the quantity b squared minus 4 a c, all divided by 2 a.
ANSWER: quadratic equation [accept quadratic formula]
[10m] These formulas, named for a 16th-century French mathematician, relate polynomial coefficients to symmetric functions of the roots. For a quadratic, they state that the sum of roots equals negative b over a.
ANSWER: Vieta’s formulas [or Viète's formulas]
[10h] Cardano’s method for solving cubics begins by transforming the equation into one of these forms, which lack the second-highest degree term. Completing the square transforms a general quadratic into this form by eliminating the linear coefficient.
ANSWER: depressed polynomial [or depressed equation or depressed cubic or depressed quadratic]
<Science - Math, Vikram Narasimhan> | VAULT II Packet 03

HeardPPBE %M %H %
4313.7298%21%19%

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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
Chattahoochee BLambert A100010E
ExhibitionNorthview B1001020EH
HooverNorthview A10101030EMH
Innovation AJohns Creek100010E
Innovation BMidtown10101030EMH
Lambert BChattahoochee A1001020EH

Summary

TournamentEditionMatchHeardPPBE %M %H %
VAULT II at Georgia Tech2026-01-24✓620.00100%33%67%
Triangle Cup2026-03-13✓310.00100%0%0%
VAULT II at Eden Prairie HS2026-03-13✓313.33100%0%33%
VAULT II at McGill2026-03-13✓36.6767%0%0%
VAULT II at UCSB2026-03-13✓512.00100%20%0%
VAULT II Northern UK2026-04-24✓310.00100%0%0%
VAULT II Southern UK2026-04-24✓310.00100%0%0%
VAULT II at Harvard2026-04-30✓417.50100%25%50%
VAULT II at MINT2026-06-19✓514.00100%40%0%
VAULT II Stanford Online2026-07-17✓815.00100%38%13%