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  2. Discriminant - Wikipedia

    en.wikipedia.org/wiki/Discriminant

    If the discriminant is positive, the number of non-real roots is a multiple of 4. That is, there is a nonnegative integer k ≤ n/4 such that there are 2k pairs of complex conjugate roots and n − 4k real roots. If the discriminant is negative, the number of non-real roots is not a multiple of 4.

  3. Discriminant of an algebraic number field - Wikipedia

    en.wikipedia.org/wiki/Discriminant_of_an...

    The discriminant of K is 49 = 7 2. Accordingly, the volume of the fundamental domain is 7 and K is only ramified at 7. In mathematics, the discriminant of an algebraic number field is a numerical invariant that, loosely speaking, measures the size of the (ring of integers of the) algebraic number field.

  4. Algebraic number field - Wikipedia

    en.wikipedia.org/wiki/Algebraic_number_field

    For this converse the field discriminant is needed. This is the Dedekind discriminant theorem. In the example above, the discriminant of the number field () with x 3 − x − 1 = 0 is −23, and as we have seen the 23-adic place ramifies. The Dedekind discriminant tells us it is the only ultrametric place that does.

  5. Integer factorization - Wikipedia

    en.wikipedia.org/wiki/Integer_factorization

    For example, 15 is a composite number because 15 = 3 · 5, but 7 is a prime number because it cannot be decomposed in this way. If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4).

  6. List of number fields with class number one - Wikipedia

    en.wikipedia.org/wiki/List_of_number_fields_with...

    All complex cubic fields with discriminant greater than −500 have class number one, except the fields with discriminants −283, −331 and −491 which have class number 2. The real root of the polynomial for −23 is the reciprocal of the plastic ratio (negated), while that for −31 is the reciprocal of the supergolden ratio .

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    Barbara Corcoran: If Mortgage Rates Hit This Number, the Market Will "Go Ballistic" 13 Cheap Cryptocurrencies With the Highest Potential Upside for You. These 11 Rare Coins Sold for Over $1 Million.

  8. Discriminant (disambiguation) - Wikipedia

    en.wikipedia.org/wiki/Discriminant_(disambiguation)

    The discriminant of a polynomial is a quantity that depends on the coefficients and determines various properties of the roots. Discriminant may also refer to its various generalizations: Mathematics

  9. Today's Wordle Hint, Answer for #1249 on Tuesday, November 19 ...

    www.aol.com/todays-wordle-hint-answer-1249...

    Today's Wordle Answer for #1249 on Tuesday, November 19, 2024. Today's Wordle answer on Tuesday, November 19, 2024, is GOING. How'd you do? Next: Catch up on other Wordle answers from this week.