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,

$a{x}^2+bx+c=0$

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 $x$.