Engineering↗
The Quadratic Formula and the Discriminant
The formula that solves every quadratic, what b2 - 4ac tells you before you compute anything, and the three cases it distinguishes.
Tag
discriminant
Every page in the KEVOS library tagged discriminant. 11 pages.
Engineering↗
Quadratic Equations by Square Roots and the Quadratic Formula
Handbook guide to quadratic equations by square roots and the quadratic formula, with rules, worked examples, verification, common errors and practical.
Engineering↗
Quadratic Formula: Solving General Quadratic Equations
Use the quadratic formula for ax²+bx+c=0, identify coefficients correctly, simplify the discriminant and interpret resulting roots.
Engineering↗
Binary Quadratic Forms and the Ideal Correspondence
The dictionary between binary quadratic forms and ideals of a quadratic order, and why the form language is computationally preferable.
Engineering↗
Discriminants and Integral Bases
The discriminant of a basis, the field discriminant, and the index-squared relation that governs maximal order computation.
Engineering↗
Galois Groups of Cubic and Quartic Fields
Complete determination of Galois groups in degrees three and four, where the discriminant and one cubic resolvent decide everything.
Engineering↗
Quadratic Field Discriminants and Integral Bases
Discriminants and integral bases of quadratic fields, given by closed formulas with no computation required.
Engineering↗
Resultants and Discriminants
The resultant as a criterion for common roots, the discriminant as a test for repeated roots, and how both are computed in practice.
Engineering↗
Solving Quadratic Congruences
Reducing a general quadratic congruence to a square root extraction, and handling the degenerate cases the reduction assumes away.
Engineering↗
Weierstrass Equations and Invariants
General and short Weierstrass forms, the discriminant and j-invariant, and the transformations relating equivalent models.
Engineering↗
The Subresultant Algorithm, Resultants and Discriminants
The subresultant polynomial remainder sequence, the resultant as a determinant and as a product over roots, the discriminant, and their use in elimination and in number field ar…
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