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If the coefficients are real numbers, the formula covers all complex solutions, not just real ones. The formula being rather complicated, it is worth splitting it in smaller formulas. Let Δ 0 = b 2 − 3 a c , Δ 1 = 2 b 3 − 9 a b c + 27 a 2 d . {\displaystyle {\begin{aligned}\Delta _{0}&=b^{2}-3ac,\\\Delta _{1}&=2b^{3}-9abc+27a^{2}d.\end ...
This is a list of unsolved problems in chemistry. Problems in chemistry are considered unsolved when an expert in the field considers it unsolved or when several experts in the field disagree about a solution to a problem.
When considering equations, the indeterminates (variables) of polynomials are also called unknowns, and the solutions are the possible values of the unknowns for which the equality is true (in general more than one solution may exist). A polynomial equation stands in contrast to a polynomial identity like (x + y)(x − y) = x 2 − y 2, where ...
A solution of a polynomial system is a tuple of values of (x 1, ..., x m) that satisfies all equations of the polynomial system. The solutions are sought in the complex numbers, or more generally in an algebraically closed field containing the coefficients. In particular, in characteristic zero, all complex solutions are sought.
14455-29-9 Al 2 Cl 9 K 3: potassium aluminium chloride: 74978-20-4 Al 2 CoO 4: cobalt blue: 1333-88-6 Al 2 F 6: aluminium fluoride: 17949-86-9 Al 2 I 6: aluminium iodide: 18898-35-6 Al 2 MgO 4: magnesium aluminium oxide: 12068-51-8 Al 2 O: dialuminium monoxide: 12004-36-3 Al 2 O 2: dialuminium dioxide: 12252-63-0 Al 2 O 3: aluminium oxide: 1344 ...
The roots of a polynomial expression of degree n, or equivalently the solutions of a polynomial equation, can always be written as algebraic expressions if n < 5 (see quadratic formula, cubic function, and quartic equation). Such a solution of an equation is called an algebraic solution.
A solution in radicals or algebraic solution is an expression of a solution of a polynomial equation that is algebraic, that is, relies only on addition, subtraction, multiplication, division, raising to integer powers, and extraction of n th roots (square roots, cube roots, etc.). A well-known example is the quadratic formula
A chemical equation is the symbolic representation of a chemical reaction in the form of symbols and chemical formulas.The reactant entities are given on the left-hand side and the product entities are on the right-hand side with a plus sign between the entities in both the reactants and the products, and an arrow that points towards the products to show the direction of the reaction. [1]