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A similar but more complicated method works for cubic equations, which have three resolvents and a quadratic equation (the "resolving polynomial") relating and , which one can solve by the quadratic equation, and similarly for a quartic equation (degree 4), whose resolving polynomial is a cubic, which can in turn be solved. [14]
Because (a + 1) 2 = a, a + 1 is the unique solution of the quadratic equation x 2 + a = 0. On the other hand, the polynomial x 2 + ax + 1 is irreducible over F 4, but it splits over F 16, where it has the two roots ab and ab + a, where b is a root of x 2 + x + a in F 16. This is a special case of Artin–Schreier theory.
With specific values for C a and K a this quadratic equation can be solved for x. Assuming [4] that pH = −log 10 [H +] the pH can be calculated as pH = −log 10 x. If the degree of dissociation is quite small, C a ≫ x and the expression simplifies to = and pH = 1 / 2 (pK a − log C a).
The quadratic equation on a number can be solved using the well-known quadratic formula, which can be derived by completing the square. That formula always gives the roots of the quadratic equation, but the solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic fraction that can be evaluated ...
Quadratic equation; Cubic equation; Biquadratic equation; Quartic equation; Quintic equation; Sextic equation; Characteristic equation; Class equation; Comparametric equation; Difference equation. Matrix difference equation; Differential equation. Matrix differential equation; Ordinary differential equation; Partial differential equation; Total ...
Here, 1 / f eq can have a fractional (non-integer) value. In precipitation reactions, the equivalence factor measures the number of ions which will precipitate in a given reaction. Here, 1 / f eq is an integer value. Normal concentration of an ionic solution is also related to conductivity (electrolytic) through the use of ...
An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula . For example, a solution of table salt , also known as sodium chloride (NaCl), in water would be represented as Na + (aq) + Cl − (aq) .
The key feature of these rate equations is that they are nonlinear; the second term on the right varies as the square of the concentration of B. This feature can lead to multiple fixed points of the system, much like a quadratic equation can have two roots. Multiple fixed points allow for multiple states of the system.