Mathematics for Chemistry/Functions

Functions as tools in chemistry

The quadratic formula

In order to find the solutions to the general form of a quadratic equation,

$ax^{2}+bx+c=0$

there is a formula

$x={\frac {-b\pm {\sqrt {(b^{2}-4ac)}}}{2a}}$

(Notice the line over the square root has the same priority as a bracket. Of course we all know by now that ${\sqrt {a+b}}$ is not equal to ${\sqrt {a}}+{\sqrt {b}}$ but errors of priority are among the most common algebra errors in practice).

There is a formula for a cubic equation but it is rather complicated and unlikely to be required for undergraduate-level study of chemistry. Cubic and higher equations occur often in chemistry, but if they do not factorise they are usually solved by computer.

Solve:

$2x^{2}-14x+9$

$1.56(x^{2}+3.67x+0.014)$

Notice the scope or range of the bracket.

$2x^{2}-4x+2$

$-45.1(1.2[A]^{2}-57.9[A]+4.193)$

Notice here that the variable is a concentration, not the ubiquitous $x$.