In mathematics, a fundamental discriminant D is an integer invariant in the theory of integral binary quadratic forms. If Q(x, y) = ax2 + bxy + cy2 is a quadratic form with integer coefficients, then D = b2 − 4ac is the discriminant of Q(x, y). Conversely, every integer D with D ≡ 0, 1 (mod 4) is the discriminant of some binary quadratic form with integer coefficients. Thus, all such integers are referred to as discriminants in this theory. There are explicit congruence conditions that give the set of fundamental discriminants. Specifically, D is a fundamental discriminant if and only if one of the following statements holds * D ≡ 1 (mod 4) and is square-free, * D = 4m, where m ≡ 2 or 3 (mod 4) and m is square-free. The first ten positive fundamental discriminants are: 1, 5, 8, 12, 13, 17, 21, 24, 28, 29, 33 (sequence in the OEIS). The first ten negative fundamental discriminants are: −3, −4, −7, −8, −11, −15, −19, −20, −23, −24, −31 (sequence in the OEIS). (Wikipedia).
How to use the discriminat to describe your solutions
👉 Learn how to determine the discriminant of quadratic equations. A quadratic equation is an equation whose highest power on its variable(s) is 2. The discriminant of a quadratic equation is a formula which is used to determine the type of roots (solutions) the quadratic equation have. T
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👉 Learn how to determine the discriminant of quadratic equations. A quadratic equation is an equation whose highest power on its variable(s) is 2. The discriminant of a quadratic equation is a formula which is used to determine the type of roots (solutions) the quadratic equation have. T
From playlist Discriminant of a Quadratic Equation
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From playlist Discriminant of a Quadratic Equation | Learn About
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👉 Learn all about the discriminant of quadratic equations. A quadratic equation is an equation whose highest power on its variable(s) is 2. The discriminant of a quadratic equation is a formula which is used to determine the type of roots (solutions) the quadratic equation have. The disc
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👉 Learn how to determine the discriminant of quadratic equations. A quadratic equation is an equation whose highest power on its variable(s) is 2. The discriminant of a quadratic equation is a formula which is used to determine the type of roots (solutions) the quadratic equation have. T
From playlist Discriminant of a Quadratic Equation
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👉 Learn all about the discriminant of quadratic equations. A quadratic equation is an equation whose highest power on its variable(s) is 2. The discriminant of a quadratic equation is a formula which is used to determine the type of roots (solutions) the quadratic equation have. The disc
From playlist Discriminant of a Quadratic Equation | Learn About
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👉 Learn how to determine the discriminant of quadratic equations. A quadratic equation is an equation whose highest power on its variable(s) is 2. The discriminant of a quadratic equation is a formula which is used to determine the type of roots (solutions) the quadratic equation have. T
From playlist Discriminant of a Quadratic Equation
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