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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.
Entrepreneurship is also sometimes considered a factor of production. [4] Sometimes the overall state of technology is described as a factor of production. [5] The number and definition of factors vary, depending on theoretical purpose, empirical emphasis, or school of economics. [6]
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.
In mathematics, especially in algebraic number theory, the Hermite–Minkowski theorem states that for any integer N there are only finitely many number fields, i.e., finite field extensions K of the rational numbers Q, such that the discriminant of K/Q is at most N. The theorem is named after Charles Hermite and Hermann Minkowski.
This implies an ideal division of the income generated from output into an income due to each input factor of production, equal to the marginal product of each input. The inputs to the production function are commonly termed factors of production and may represent primary factors, which are stocks. Classically, the primary factors of production ...
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).
These can be found in terms of the discriminant of Q. For example, in the case x 2 + x + 2 given above, the discriminant is −7 so that 7 is the only prime that has a chance of making it satisfy the criterion. Modulo 7, it becomes (x − 3) 2 — a repeated root is inevitable, since the discriminant is 0 mod 7. Therefore the variable shift is ...
This example of production holds true to this common understanding as production is subject to the four factors of production which are land, labour, capital and enterprise. [8] These factors have the ability to influence economic growth and can eventually limit or inhibit continuous exponential growth. [ 9 ]