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
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 43 | 13.72 | 98% | 21% | 19% |
Conversion
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| VAULT II at Georgia Tech | 2026-01-24 | ✓ | 6 | 20.00 | 100% | 33% | 67% |
| Triangle Cup | 2026-03-13 | ✓ | 3 | 10.00 | 100% | 0% | 0% |
| VAULT II at Eden Prairie HS | 2026-03-13 | ✓ | 3 | 13.33 | 100% | 0% | 33% |
| VAULT II at McGill | 2026-03-13 | ✓ | 3 | 6.67 | 67% | 0% | 0% |
| VAULT II at UCSB | 2026-03-13 | ✓ | 5 | 12.00 | 100% | 20% | 0% |
| VAULT II Northern UK | 2026-04-24 | ✓ | 3 | 10.00 | 100% | 0% | 0% |
| VAULT II Southern UK | 2026-04-24 | ✓ | 3 | 10.00 | 100% | 0% | 0% |
| VAULT II at Harvard | 2026-04-30 | ✓ | 4 | 17.50 | 100% | 25% | 50% |
| VAULT II at MINT | 2026-06-19 | ✓ | 5 | 14.00 | 100% | 40% | 0% |
| VAULT II Stanford Online | 2026-07-17 | ✓ | 8 | 15.00 | 100% | 38% | 13% |