Search results
Results From The WOW.Com Content Network
In algebra, a cubic equation in one variable is an equation of the form + + + = in which a is not zero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation.
Casus irreducibilis (from Latin 'the irreducible case') is the name given by mathematicians of the 16th century to cubic equations that cannot be solved in terms of real radicals, that is to those equations such that the computation of the solutions cannot be reduced to the computation of square and cube roots.
In mathematics, an Abel equation of the first kind, named after Niels Henrik Abel, is any ordinary differential equation that is cubic in the unknown function. In other words, it is an equation of the form
Suppose that the equation y 2 = x 3 + a x 2 + b x + c {\displaystyle y^{2}=x^{3}+ax^{2}+bx+c} defines a non-singular cubic curve with integer coefficients a , b , c , and let D be the discriminant of the cubic polynomial on the right side:
Cubic equations, which are polynomial equations of the third degree (meaning the highest power of the unknown is 3) can always be solved for their three solutions in terms of cube roots and square roots (although simpler expressions only in terms of square roots exist for all three solutions, if at least one of them is a rational number).
The impossibility of straightedge and compass construction follows from the observation that is a zero of the irreducible cubic x 3 + x 2 − 2x − 1. Consequently, this polynomial is the minimal polynomial of 2cos( 2π ⁄ 7 ), whereas the degree of the minimal polynomial for a constructible number must be a power of 2.
Using only one rib is such cases could lead to a dish with a much milder flavor than intended. Adding to the complexity, the number of ribs in a stalk can vary significantly depending on the size ...
Formally, if one expands () (), the terms are precisely (), where is either 0 or 1, accordingly as whether is included in the product or not, and k is the number of that are included, so the total number of factors in the product is n (counting with multiplicity k) – as there are n binary choices (include or x), there are terms ...