Packet I: Tossup 18

For an algebraic number field K, a quantity of this name determines which primes ramify K and equals the determinant (10[1]-5[1])of a trace pairing matrix. For a polynomial, this noun denotes the product of all squared differences between pairs of roots. (10[1])This noun appears in the name of a supervised learning (10[1])method that finds (10[1])weighted sums of features that maximize the ratio of between (-5[1])and within-class variances; that linear (10[1])method was developed by Fisher. A complicated (-5[1])quantity of this name that includes the term “27 a-squared (10[1])d-squared” (10[2])appears in the (-5[1])innermost (-5[1])square (10[1])root (10[2])in Cardano’s (10[1])formula. (10[1]-5[2])The sign of a quantity of this name determines (-5[1])the number (10[1]-5[1])of roots (10[3])of (-5[1])a quadratic polynomial. (10[3]-5[2])For 10 (-5[1])points, (10[2]-5[1])what (-5[1])noun (10[1]-5[1])denotes the quantity (10[1])“b-squared (10[1])minus (10[1]-5[1])4 (10[1]-5[1])a (-5[2])c” (10[8]-5[3])in the (10[1])quadratic (10[2])formula? (10[1])■END■ (10[13]0[12])

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