Determinantes de Hurwitz para verificar quando polinômios possuem somente raízes reais
Bibliographic record
Abstract
When it comes to polynomial equations, the mathematician Sridhara in the twelfth century determined the current formula for solving quadratic equations, known as Bhas kara.In 1545 Girolamo Cardano published the method for solving equations of the third and fourth degree currently known as the Cardano-Tartaglia method.But it was the French mathematician E. Galois who, upon completing Abel's work, showed that a solution by radicals for polynomial equations of degree greater than four is not possible.Based on the above context, it is easy to know if a polynomial of degree less than or equal to four has only real roots, in this way, using the Hurwitz Matrices, we will approach the method that verifies when a polynomial of any degree has only real roots and confront this method with the solutions by radicals of the equations of degree: two, three and the biquadratic equation.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".