Question

This adjective denotes a type of imaginary field of which there exist nine with unique factorization, which is the “n equals one” case of the class number problem. An integer x is a type of number denoted by this adjective with respect to a prime p if and only if x to the “p-minus-one over 2” is congruent to one mod p, by (-5[1])Euler’s criterion. A result with this adjective in its name concerns the Legendre symbol of “p over q” times the Legendre symbol of “q over p.” That theorem about modular congruences, which can be used to find “residues” described by this adjective, (10[1])was proved by Gauss and is named for this type of “reciprocity.” (10[2])This adjective denotes a formula whose discriminant is “b-squared minus 4 a c.” (10[2])For 10 points, what adjective denotes polynomials whose leading term is x-squared? ■END■ (10[1])

ANSWER: quadratic [accept quadratic number field; accept quadratic residue; accept quadratic reciprocity; accept quadratic formula or quadratic equation]
<TM, Other Science>
= Average correct buzz position

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Buzzes

PlayerTeamOpponentBuzz PositionValue
Yashwanth BajjiMichigan AKenyon62-5
Leo TaoMichigan CCarnegie Mellon A10410
Calvin BostlemanOhio State AMichigan D11610
Aditya PatnaikOhio State BCarnegie Mellon B11610
Angelo PanCase Western BMichigan B12910
Sai SubramanianCase Western AMichigan State12910
Noah DeanKenyonMichigan A14210

Summary

Great Lakes2025-02-01Y6100%0%17%122.67
Lower Mid-Atlantic2025-02-01Y1100%0%0%127.00
Midwest2025-02-01Y1100%0%0%83.00
Northeast2025-02-01Y3100%0%0%67.00
Overflow2025-02-01Y4100%0%25%126.00
Pacific Northwest2025-02-01Y2100%0%0%127.00
South Central2025-02-01Y250%0%50%117.00
UK2025-02-01Y1100%0%100%142.00